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THE  LIBRARY 

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ilium 


Practical  Harmony 


HomerA.Norris 
Part  I 


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P-n  MUSIC 

oU  LIBRARY 

V.l 


Southern  Branch 
of  the 

University  of  California 

music  ~    Los  Angeles 

LIBRARY 
Form  L-l 

MT50 


Practical  Harmony 

A  COMPREHENSIVE  SYSTEM  OF  MUSICAL  THEORY 
ON  A  FRENCH  BASIS 


BY 

HOMER  A.   NORRIS 


Part  I.  Consonance  Part  II.  Dissonance 

Part  III.  Key  to  Harmony 


PHILADELPHIA 

THEODORE    PRESSER   CO. 


4-o-a  ^b^> 


Copyright,  1894, 
BY 

H.  B.  Stevens  Company 
Boston 


Copyright  secured  in  England 


Copyright  transferred,  1903,  to 
Theo.  Presser 


/ 


MUSIC 
f.lBRARY 

H7^f 


PREFACE. 


» 

The  author  has  endeavored  to  prepare  a  text-book  on  harmony, 
based  on  the  principles  of  the  most  eminent  French  theorists  and 
composers,  which  shall  enable  the  student  to  analyze  with  ease  and 
clearness  the  most  complex  musical  compositions  of  the  modern 
school,  and  which  shall  also  stimulate  the  musical  instincts  of  those 
who  are  endowed  with  the  gift  for  composition. 

It  is  justly  urged  against  the  average  text-book  on  harmony,  that 
it  is  either  too  elementary  or  too  scientific.  If  too  elementary,  it 
leaves  the  pupil  uninformed  regarding  much  that  he  will  meet  in  the 
works  of  the  masters,  and  it  usually  contains  detail  which  fatigues 
and  discourages.  If,  on  the  other  hand,  the  book  sets  out  with 
details  of  the  laws  of  acoustics,  it  appeals  more  to  the  mathe- 
matician than  to  the  musician  :  the  theoretical  is  developed  at  the 
expense  of  the  practical,  and  neither  artistic  intelligence  nor  mu- 
sical sentiment  is  quickened.  Whatever  may  be  proved  by  such 
mathematical  calculation,  it  has  little  or  nothing  to  do  with  aes- 
thetics which  is  constantly  changing.  Our  modern  musical  system 
is  based  on  what  is  both  natural  and  artificial ;  it  has  been  accepted, 
and  our  musical  habits,  so  to  speak,  and  much  that  we  call  musical 
instinct,  are  the  result.  New  musical  effects  come,  we  suspect,  as 
a  spontaneous  discovery,  rather  than  as  a  result  of  patient  scientific 
investigation.  For  this  reason,  in  all  matters  having  to  do  with  tho 
artistic  and  the  aesthetic,  practice  should  precede  theory. 

The  study  of  harmony  can  be  made,  and  should  be  made,  not  a 
drudgery,  but  a  delight ;  and  the  French  methods  have  been  chosen 
as  a  basis  for  this  book,  because  they  present  theories  in  an  attrac- 
tive, as  well  as  in  a  practical  manner. 

The  Frenchman  is  instinctively  an  artist.  The  beautiful  appeal;- 
to  him  irresistibly,  and  his  feeling  for  the  narrow  line  that  separates 
the  commonplace  from  the  purely  artistic  is  sensitively  keen.  One 
proof  of  this  may  he  found  in  the  many  beautiful  examples  by 
eminent  French  composers  and  theorists,  written  expressly  for  this 

(iii) 


iv  PREFACE. 

book,  and  which  appear  in  Part  II.  If  one  were  not  told,  one  would 
not  suspect  that  they  were  "harmony-exercises." 

The  laws  governing  key-relationship  and  all  that  should  be 
understood  by  tonality  —  that  element  of  modern  music  which  is  of 
the  very  first  importance  —  have  been  emphasized.  A  text-book 
cf  to-day  should  make  it  clear  that  Wagner,  Brahms,  Leoncavallo, 
and  Bruneau  are  as  truly  in  key  as  is  Mozart.  It  is  believed  that 
this  can  be  most  speedily  and  most  safely  accomplished  by  first 
demonstrating  all  possible  uses  of  the  diatonic  triads. 

So  far  as  the  author  knows,  there  is  no  book  published  in  this 
country  which  reduces  the  so-called  "•Augmented  Sixth"  chords,  the 
stumbling  block  of  all  harmony  students,  to  altered  Dominant  Seventh 
chords.  He  feels  certain  that  with  this  system  they  will  be  readily 
recognized,  and  what  is  of  the  greatest  importance,  that  their  tonal 
relationship  will  be  apparent.  Moreover,  by  this  method  the  works 
of  the  masters  can  be  analyzed  much  more  easily  and  clearly. 

The  svstem  of  a  figured  bass  has  been  adhered  to  in  the  opening 
chapters,  in  order  that  the  pupil,  before  being  thrown  wholly  on  his 
own  resources,  may  gain  a  certain  facility  in  correct  writing. 
Terms  in  common  usage  have  been  employed  wherever  possible. 

The  chapters  are  divided  in  keeping  with  the  subjects  discussed ; 
the  length  of  the  lessons  must  be  left  to  the  discretion  of  the  student 
or  of  the  teacher.  A  small  pamphlet,  intended  for  teachers,  and 
containing  all  the  exercises,  with  the  harmonies  of  the  composei*s, 
is  issued  separately. 

The  author  desires  to  express  his  appreciation  of  the  warm  words 
of  encouragement,  and  of  the  suggestions  sent  from  time  to  time 
during  the  writing  of  this  book,  by  his  Paris  teachers :  Messieurs 
Theodore  Dubois,  Eugene  Gigout,  Alexandre  Guilmant  and 
Benjamin  Godard.  He  also  acknowledges  his  indebtedness  to  the 
various  text-books  used  at  the  Paris  Conservatorv,  and  notably  to 
the  Treatise  by  Reber,  with  the  accompanying  "Notes  et  Etudes" 
by  Theodore  Dubois. 

The  author  claims  little  or  nothing  that  is  new  ;  the  book  is  rather 
a  compilation  or  condensation  of  that  which  he  believes  to  be  the 
best.  It  is  hoped  that  among  the  really  good  books  on  this  subject 
it  will  find  a  welcome  place  and  add  something  which,  may  be  of 
use  to  the  modern  student.     m 

Uoston,  August,  j8yj. 

THE  AUTHOR. 


CONTENTS. 


PART  I. 

CONSONANCE. 

Chapter  1  page  i 

Note. —  Intervals, —  Inversion  of   Intervals, —  Classification  of   Inter- 
vals,—  Exercises, —  Suggestions. 


Chapter  II.  page  8 

The  Major  Mode, —  Chords, —  Triads, —  Part-writing, —  Melodic 
Progression, —  Harmonic  Progression,  —  Consecutive  Octaves  and 
Fifths, —  The  Tritone, —  .Sequence, —  RulesTor  harmonizing  Basses, — 
Suggestions, —  Exercises, —  Additional  Exercises. 


Chapter  III.  page  23 

The  Minor  Mode, —  Melodic  and  Harmonic  Progression  in  the  Minor 
Mode, —  The  Augmented  Second, —  Suggestions, —  Exercises, —  Addi- 
tional Exercises. 


Chapter  IV.  PAGE  29 

Chord-relation, —  Harmonizing  Melodies  in  the  Major  Mode, —  Sug- 
gestions,—  Harmonizing  Melodies  in  the  Minor  Mode. 


Chapter  V.  page  34 

Figuring  of  the  Bass, —  Open  Harmony, —  Exercises. 


Chapter  VI.  PAGK  j, 

Chords, —  The    First    Inversion, —  Exercises, —  Note   concerning   the 
Study  of  Counterpoint. 


Chapter  VII  page  44 

Chords, — The    Second    Inversion,  —  Observations    concerning    the 
Terms  Consonance,  and  Dissonance. 

(v) 


vj  CONTENTS. 

Chapter  VIII.  pagb  54 

Form, —  The  Phrase, —  The  Period, —  Cadence, —  Exercises. 


Chapter  IX.  page  59 

Modulation, —  Tonal  Relation, —  Modulations  of  the  First  Order, — 
Exercises, —  Modulations  of  the  Second  Order, —  Modulations  to  Re- 
mote Keys,  —  Passing  Modulations,  —  Exercises,  —  Harmonic  Se- 
quence,—  Exercises, —  Tonal  Sequence, —  Exercises. 


Chapter  X.  page  f& 

Resume.  Notation, —  Chromatic  Scale, —  The  Ecclesiastical  Scales,— 
Chords,  —  Triads,  —  Melodic  Progression,  —  Omission  of  Voices, — 
Consecutive  Fifths  and  Octaves, —  Hidden  Fifths, —  The  Tritone, — 
The  Augmented  Second, —  Tonality, —  Form, — The  First  Inver- 
sion,—  Modulation. 


PRACTICAL  HARMONY. 


PART  I. 


CONSONANCE. 


CHAPTER  I. 

Note.  The  only  elementary  knowledge  of  music  presupposed 
is  that  necessary  to  sing  or  to  play,  unaided,  a  written  melody  of 
the  simplest  order. 

INTERVALS. 

The  distance  from  one  note  to  another  is  called  an  ititerval. 

Intervals  are  reckoned  upwards,  and  are  measured  by  the 
number  of  degrees  they  occupy. 

By  degrees  is  understood  the  lines  and  spaces  of  the  staff-'. 

The  interval  at  a,  in  example  i,  is  a  fourth;  from  C  to  F,  inclu- 
sive, there  are  four  degrees.  The  interval  at  b  is  a  sixth,  and  that  at 
c  a  ninth. 


Ex.  1 


I 


W 


=t 


-<s<- 


W^ 


An  interval  is  harmonic  when  two  tones  are  heard  simultane- 
ously, melodic  when  heard  successively. 


Harmonic. 


V  Melodic. 


1 


:x.2.fp 


<y 


-O 


II 


-& 


-&- 


Intervals  are  named  either  perfect,  major,  minor,  augmented,  or 
diminished;  they  may  also  be  doubly-angmentcd,  or  doubly-dimin- 
ished. 

The  interval  from  the  first  note  of  any  major  scale  to  any  note  of 
the  same  scale  is  said   to  he  major,    excepting   the   fourth,  fifth,   and 


PRACTICAL    HARMONY. 


eighth,   which  are    perfect.      Reasons    for  naming   some  intervals 
major  and  others  perfect  will  be  given  later. 

Major.     Major.   Perfect   Perfect    Major.      Major.    Perfect    Major, 
second,    third,      fourth,     fifth.        sixth,     seventh,    eighth,     ninth. 


A  major  or  perfect  interval  made  one  half-step  larger  is  said  to 
be  augmented.  If  the  second  note  of  any  interval  in  example  3 
were  raised  one  half-step,  or  the  first  note  lowered  the  same  dis- 
tance, the  interval  would  be  augmented. 

Major  intervals  made  one  half-step  smaller  are  named  minor; 
perfect  intervals  made  one  half-step  smaller  are  named  diminished. 

Intervals  are  usually  reckoned  to  ninths,  but  when  larger  than 
a  ninth  they  are  reckoned  as  if  the  lower  note  were  placed  one  octave 
higher ;   a  tenth  would  be  called  a  third,  an  eleventh  a  fourth,  etc. 

Two  notes  standing  on  the  same  degree,  though  not  properly 
forming  an  interval,  are  classed  as  such,  and  called  a  prime. 
When  one  of  the  notes  of  a  prime  is  raised  it  becomes  an  interval 
and  is  classified  as  such. 


Perfect  Prime. 


Ex.  4. 


i 


Unison. 


Augmented  Prime. 


Interval. 


B 


A  chromatic  interval  occupies  the  same  degree.  A  diatonic 
interval  occupies  contiguous  degrees.  An  enharmonic  interval  is 
a  different  notation  of  the  same  sound  as  given  bv  an  organ  or 
a  piano. 


Chromatic.      V      Diatonic.       V  Enharmonic. 


Ex.  5. 


6 


¥- 


'-%: 


3  i^=iZ- 


~<s 


:fc 


:f= 


1 


RULE    FOR    MEASURING    INTERVALS. 
Consider  the   lower  note  as   the   first  of  a   major  scale.     If  the 


PKA  C  TIC  A  L    HA  KMONY. 


/ 


3 


upper  note  stands  in  the  scale  of  the  lower,  I.e.,  if  it  is  the 
natural,  sharped,  or  Hatted  note  necessary  to  that  key,  the  interval 
is  either  perfect  or  major. 

The  interval  at  a,  example  6,  is  a  perfect  fifth.  Taking  F  as  the 
first  of  a  major  scale,  C  natural  would  be  required  for  its  fifth ; 
fifths  are  perfect  if  the  upper  note  stands  in  the  key  of  the  lower. 

Reckoning  in  this  way,  the  interval  at  b  is  a  perfect  fourth,  and 
that  at  c  a  perfect  octave. 


a.  Perfect  fifth.       b.  Perfect  fourth,     c.  Perfect  Octave. 


Ex.  6. 


si- 


I 


All  intervals  of  the  major  scale,  excepting  the  perfect  fourth,  the 
perfect  fifth,  and  the  perfect  octave,  are  major.  Following  this  rule 
all  the  intervals  in  example  7  are  major. 


Ex.  7. 


Major  second.         Major  third.         Major  sixth.         Major  seventh. 

ffig 


-o- 


3=5^= 


ifta: 


m 


Any  perfect  or  major  interval  made  one  half-step  larger  becomes 
augmented. 


Augmented  intervals. 


Ex.  8. 


_V_._   **  -*L.-  **'  _^Ll_  _^-j_  _-*rj_ 


-<>%,&   ^&-*&   -&m      -&-         -<s*-         -&- 

Prime.     Second.-  Third.   Fourth.       Fifth.     Sixth.  Octave.  Ninth. 


The  augmented  seventh,  having  more  the  character  of  an  enhar- 
monic interval,  is  not  included. 

Any  perfect  or  minor  interval  made  one  half-step  smaller  be- 
comes diminished.      The  diminished  intervals  most  commonly  used 


are  the  following; : 


E*  9 1  i^LJ^feyi^N^lgl^FII 


rs-  go-"    -o  "go-     -<9-  $0      *    8* 

1'hird.     Fourth.     Fifth.       Sixth.       Seventh.  Octave. 


a  PRACTICAL   HARMONY. 

The  diminished  second,  having  more  the  character  of  an  enhar- 
monic interval,  is  not  included.  Diminished  primes  and  octaves 
occur  in  melodic  progressions,  but  are  not  used  in  the  construction 
of  chords  in  elementary  harmony. 

A  diminished  interval  made  one  half-step  smaller  becomes  doubly- 
diminished  ;  an  augmented  interval  made  one  half-step  larger  be- 
comes doubly-augmented.  These  intervals  are  not  often  found  in 
the  writings  of  the  older  masters,  but  are  of  frequent  occurrence  in 
modern  chromatic  harmony. 


Doubl y-aug.  fourth.     Doubly-dim.  sixth. 


Ex.   10. 


z 


-& 


%^ 


— I- 

■8St 


:{fe 


It  will  be  noticed  that  intervals  may  contain  the  same  number  of 
steps,  and  sound  the  same  when  played  on  a  piano  or  organ,  and 
yet  bear  different  names. 


Ex.   1 


Aug.    second.  V      Minor  third. 


If  in  naming  an  interval  the  lower  note  is  impracticable  for  the 
beginning  of  a  scale,  as  Ffr,  B#,  D£,  etc.,  move  both  notes  either  up 
or  down  one  half-step  without  changing  the  letters,  as  at  b  and  d 
in   example  1  2  ;   this  will  give  the  same  relative  distance. 


Ex.   12. 


INVERSION    OF    INTERVALS. 


An  interval  is  said  to  be  inverted  when  the  position  of  the  notes 
is  so  changed  that  the  one  which  was  the  lower  becomes  the  higher. 


Ex.   13. 


-Q.- 


-> 


1 


Third. 


Inversion  of  third. 


PRACTICAL   HARMONY.  e 

All  intervals,  except  those  called  perfect,  change  their  character 
by  inversion:  major  intervals  become  minor.,  and  vice  versa;  the 
diminished  become  augmented,  and  vice  versa.  The  perfect 
fourth  and  perfect  fifth  are  the  only  intervals  that  remain  the  same 
when  inverted,  and  this  is  one  reason  why  they  are  called  perfect. 
The  unison  by  inversion  becomes  a  perfect  octave,  and  is  also  classed 
a  perfect  interval.  A  few  theorists  name  the  perfect  intervals 
major.  As  they  stand  in  the  regular  order  of  the  major  scale  the_y 
are  certainly  major,  but  they  alone  remain  unchanged  by  inversion, 
and  for  this  reason,  as  well  as  for  others  that  will  appear  later,  it  is 
better  to  give  them  a  more  specific  name.  Moreover,  these  inter- 
vals are  termed  perfect  by  the  more  prominent  theorists,  and  it  is 
always  best  to  follow  tradition  unless  some  great  advantage  is  gained 
by  a  change. 

CLASSIFICATION    OF    INTERVALS. 

There  are  certain  intervals  which  at  once  please  the  ear  and  give 
a  sense  of  repose  or  finality.  The  most  important  are  the  fifth  and 
octave  which  are  termed  in  musical  theory  the  perfect  consonances. 

The  next  in  importance  are  the  major  and  minor  thirds  and 
sixths ,   these  are  termed  the  imperfect  consonances. 

The  interval  of  the  fourth  is  classed  by  the  best  theorists  a  mixed 
or  neutral  interval ;  it  is  sometimes  consonant,  sometimes  dissonant, 
according  to  the  position  it  holds.  Theoretically  it  may  be  con- 
sidered a  perfect  consonance,  but  musically  never,  because  few 
intervals  give  a  less  sense  of  repose  or  finality  than  the  fourth. 
At  one  time  it  was  considered  one  of  the  most  perfect  of  intervals, 
later  as  a  dissonance.  This  suggested  that  it  might  be  either  one  or 
the  other  according  to  conditions,  and  so  it  is  now  named  a  mixed 
interval.  This  will  be  more  fully  explained  in  the  chapter  on  the 
inversion  of  chords. 

In  writing  ascending  passages  of  half-steps  it  is  correct,  as  a  gen. 
eral  ride,  to  use  sharps,  as  at  a  in  example  14;  in  descending  pas* 
sages  it  is  correct,  as  a  general  rule,  to  use  flats,  as  at  b. 


Ex.    14 


6  PRACTICAL   HAKMOXY. 

Played  on  a  piano  or  organ  the  QJ  at  a  gives  precisely  the  same 
sound  as  the  Di?  at  b ,  but  played  on  a  violin  or  any  instrument  that 
gives  a  pure  scale,  the  CJJ  is  higher.  For  this  reason  sharps  natu- 
rally ascend  and  flats  descend.  From  C  to  Q%  is  called  a  large  half- 
step,  from  C  to  Di?  a  small  half-step.  In  other  words,  a  chromatic 
semitone  forms  a  large  half-step,  a  diatonic  semitone  a  small  half- 
step. 

EXERCISES. 

Copy  the  following  notes  on  a  staff*  and  above  each  write  the  in- 
terval called  for. 


i 


Chromatic    Diatonic  Enharmonic    Small         Large 
Unison.  Aug.  prime,  semitone,  semitone,    interval.      half-step,   half-step. 


_£k_ 


^m 


■$z: 


g 


Major  second.     Minor  second.     Aug.  second.      Major  third.     Minor  third. 


~w&* 


Aug.  third.     Diminished  third.     Perfect  fourth.     Aug.  fourth.     Dim.  fourth. 


Effi 


-te- 


-«s>- 


I 


Doubly-aug  fourth.  Perfect  fifth.      Dim.  fifth.      Aug.  fifth.     Doubly-dim.  fifth. 

-  =i=  =l=iE===l 


c- 


-\>zr 


Major  sixth.        Minor  sixth.       Aug.  sixth.         Dim.  sixth.       Major  seventh. 


Il^^l! 


<< 


Minor  seventh.      Dim.  seventh.  Perfect  octave.  Dim.  octave. 


3£: 


$ 


Aug.  octave.        Major  ninth. 


Z&r 


Minor  ninth. 


& 


Aug.  ninth. 


I 


I 


PRACTICAL    HARMONY.  7 

JVbte.  The  diminished  fourth  and  fifth  are  often  called  i?nper- 
fect  intervals,  to  distinguish  them  from  the  perfect.  The  terms 
imperfect  and  diminished  are  synonymous  in  speaking  of  the 
fourth,  fifth,  and  octave. 

SUGGESTIONS. 

The  student  is  urged  at  this  point  to  name  the  intervals  in  any 
standard  piece  of  music.  For  this  exercise  nothing  could  be  more 
exhaustive  than  the  overture  to  Wagner's  Tristan  and  Isolda, 
which  may  be  found  in  inexpensive  edition  at  any  music  store. 

This  exercise  is  for  the  eye  only,  and  it  is  the  teacher's  duty 
to  see  that  the  ear  is  likewise  trained,  for  it  is  of  the  greatest  impor- 
tance that  the  student  realize  at  the  beginning  that  he  should  hear 
as  well  as  see. 

One  of  the  most  practical  exercises  is  for  the  teacher  to  play  or 
sing  a  melody  which  the  pupil  should  notate  on  black-board  or 
music  paper.  It  is  best  to  play  or  singthe  melody  slowlv,  and  with 
as  little  accent  as  possible  ;  in  this  way  it  becomes  a  valuable  exer- 
cise in  rhythm.  Unless  the  pupil  has  absolute  pitch,  it  will  he 
found  necessary  at  first  to  name  the  key  in  which  the  melody  is 
played  or  sung.  It  is  best  to  play  a  short  phrase  three  times,  with 
a  slight  pause  between  the  first  two  hearings,  but  connecting  the 
phrase  the  third  time  to  the  succeeding  phrase.  The  pupil  should 
notate  all  of  the  phrase  he  can  hear  before  the  third  repetition. 
After  the  whole  has  been  notated,  the  teacher  should  play  it  through 
slowlv,  the  pupil  correcting  the  errors  as  best  he  can. 

With  a  few  exceptions  this  exercise  will  be  found  discouraging 
to  the  student  at  the  beginning;  a  few  lessons  will  show  surprising 
results,  and  later  he  will  realize  the  great  advantage  of  such  an 
acquisition. 

Another  useful  exercise  is  for  the  student  to  write  any  intervals 
he  may  choose.  The  teacher  may  play  them  either  correctly  or 
not,  and  the  student  must  decide  whether  or  not  they  are  played  as 
written. 

For  all  work  of  this  character  the  black-board  is  more  useful 
than  music-paper. 

The  pupil  will  save  much  time  if  he  will  acquire  the  following 
method  of  notating  :  In  making  a  whole  note  draw  the  upper  half 
from  right  to  left:    •^N,  then  add  the  lower  half  from   right  to  left: 


PRACTICAL  HARMONY. 


O.      In  making  a  half  note  a  stem  only  need  be  added:    J.     This 

method  not  only  insures  greater  facility  of  execution  but  elegance 
of  notation.      Whenever  a  single  note    stands  above   the    third  line 

the  stem  should  extend  downwards  :  :L^— •  Whenever  a  note  stands 


below  the  third  line  the  stem  should  extend  upwards 


CHAPTER   II. 

SCALES. 

THE  MAJOR  MODE.     TRIADS.     PART-WRITING.     MELODIC  PROGRESSION.     HARMONIC 
PROGRESSION.     CONSECUTIVE  OCTAVES  AND  FIFTHS.     THE  TRITONE.     SEQUENCE 

The  form  of  the  major  scale  as  used  to-day  has  remained  fixed  foi 
about  two  centuries. 

It  consists  of  a  succession  of  major  and  minor  seconds,  the  lattei 
coming  only  between  the  third  and  fourth,  and  the  seventh  and  eighth 
degrees  of  the  scale.  A  scale  with  the  above  succession  of  intervals 
is  said  to  be  in  the  major  mode,  and  diatonic. 


Ex.    1  5. 


I 


m 


-^r-*^2- 


~&- 


/»?- 


<S>—& 


Unless  the  student  is  thoroughly  familiar  with  all  the  major  scales 
he  should  now  write  one  from  each  of  the  following  notes  :  C,  G, 
D,  A,  E,  B,  F#,  Gtf,  Cb,  Gb,  Db,  Ab  Eb,  Bb,  and  F.  Place  no 
sharps  or  flats  at  the  beginning  of  any  scale,  but  insert  them, 
wherever  necessary,  preserving  the  same  order  of  intervals  as  is 
given  in  Ex.  i  5. 

CHORDS. 

By  the  word  chord  is  meant  the  simultaneous  sounding  of  differ- 
ent tones. 

Chords  are  built  by  taking  any  note  and  adding  above  it  a  succes- 
sion of  thirds.     The  lowest  note  is  called  the  root  or  fundamental 


PRACTICAL    HARMONY. 


In  example  16,  G  being  the  lowest  note,  and  those  above  formed 
in  a  series  of  thirds,  G  is  the  root  or  fundamental  of  each  chord. 


Ex.   16. 


i 


-s>- 


^ 


i 


-<s>- 


1 


To  find  the  root  of  any  chord,  arrange  the  notes  so  that  they  be- 
come a  succession  of  thirds  ;  the  lowest  note  will  always  be  the  root 
or  fundamental. 

In  example  17,  E  is  not  the  root  of  the  chord  at  a,  because  the 
interval  from  the  second  note  of  the  chord,  G,  to  the  next,  C,  is 
not  a  third  but  a  fourth.  Rearrange  these  notes,  as  at  <$,  in  a  series 
of  thirds,  and  the  root  is  found  to  be  C. 

a.  b. 


Ex.   17 


i 


J2- 


% 


-<§— 


-&- 


Chords  are  reckoned  in  this  way  containing  three,  four,  and  five 
notes ;  those  of  more  than  five  notes,  or  aggregations  that  cannot 
be  readjusted  in  thirds,  will  be  explained  later. 

EXERCISES. 
Name  the  roots  of  the  following  chords  : 


Ex.   18. 


<&— 


o 


TT 


<"> 


m 


-O.- 


r> 


-&- 


-0- 


jO- 


-G>- 


J2- 


sr 


Sr 


m 


% 


1 


j  ,  1   1- 


& 


-a- 


-<2- 


=^ 


fcg 


9 — — 1— ?h 


V 


I 


TRIADS. 

A  chord  formed  of  three  notes  is  named  a  triad. 

This  chord  forms  the  basis  of  all  musical  composition,  and  for 
that  reason  will  be  used  exclusively  in    Part  I.  of  this  book. 

Triads,  like  intervals,  are  either  major,  minor,  diminished,  or  aug- 
mented.    A  triad  may  be  formecton  any  degree  of  the  scale. 


IO 


PR  A  C  TIC  A  L   HA  RMONY. 


Each  triad  is  formed  by  adding  a  third  and  a  fifth  to  any  note 
taken  as  a  root ;  the  distance  of  these  upper  notes  from  the  ix>ot  de- 
termines the  character  of  the  triad;  i.e.,  whether  it  be  major, 
minor,  diminished,  or  augmented. 

A  major  third  and  perfect  fifth  form  a  major  triad. 

A  minor  third  and  perfect  fifth  form  a  minor  triad, 
l  A  minor  third  and  diminished  fifth  form  a  diminished  triad. 

A  major  third  and  augmented  fifth  form  an  augmented  triad. 

Roman  numerals  beneath  chords  show  upon  which  degree  of  the 
scale  they  are  founded.  The  different  kinds  of  triads  are  usually  dis- 
tinguished in  this  way :  large  numerals  denote  major  triads,  small 
numerals  denote  minor  triads.  A  zero  (o)  by  the  side  of  a  small 
numeral  denotes  a  diminished  triad,  and  the  plus  sign  (x)  denotes 
an  augmented  triad. 

The  different  kinds  of  triads  found  in  the  major  scale  would  be 
distinguished  by  Roman  numerals  as  follows  : 


Ex.    19. 


Major.  Minor.    Minor.  Major.  Major.  Minor.     Dim. 


'7S~ 
II 


^ 


-&- 


I £2- 


-3- 


-<S- 


-<S2_ 


S 


D 


in 


IV       v 


VI 


vir 


For  convenience  in  speaking,  and  also  partly  to  indicate  the  rela- 
tive importance  of  chords,  special  names  have  been  given  to  each 
note  of  tie  scale. 

The  following  is  the  order  preferred  by  many  theorists: 


Tonic 

Super-tonic- 
Mediant 


-ist  degree  of  scale. 
-2d  degree  of  scale. 
-3d  degree  of  scale. 


Sub-dominant — 4th  degree  of  scale. 

Dominant 5th  degree  of  scale. 

Sub-mediant 6th  degree  of  scale. 

Leading-tone *]\\\  degree  of  scale. 

The  major  chords  are  the  most  important  and  are  called  the  pri- 
mary or  principal  triads  There  are  but  three,  those  built  on  the 
tonic  (  I  ),  dominant  (  V),  and  sub-dominant  {  IV  ).  In  this  book 
the  terms  super-tonic,  mediant,  and  sub-mediant,  will  not  be  used  ; 
those  degrees  will  be  called  respectively  the  second,  third,  and 
sixth.     A  musician  rarely  speaks  of  them   in  any  other  way,   this 


PR  A  C  TIC  A  L   HA  RMONY. 


II 


distinction  making  prominent  the  more  important  triads.  The 
term  leading-tone  will  be  used  in  speaking  of  the  seventh  degree 
of  the  scale. 

The  triads  on  the  second,  third,  and  sixth,  to  distinguish  them 
from  the  primary  triads,  are  called  the  secondary  triads.  Both  the 
primary  and  secondary  triads  are  consonant ;  the  triad  on  the  lead- 
ing-tone, including  the  diminished  fifth,  will  be  classed  later. 

PART-WRITING. 
DOUBLING    OF    VOICES. 

In  the  study  of  harmony  the  student  should  always  write  for 
voices,  unless  otherwise  directed,  and  usually  for  a  mixed  chorus  of 
four  parts,  —  soprano,  alto,  tenor,  and  bass.  These  voices  should 
rarely  exceed  the  limits  given  below. 


Soprano 


Ex.  20. 


In  writing  four-part  harmony,  as  there  are  but  three  notes  in  a 
triad,  one  of  these  notes  must  be  doubled  or  used  twice.  Any  note 
of  a  triad  may  be  doubled,  but  it  is  better  to  double  the  root  than 
the  fifth,  and  better  to  double  the  fifth  than  the  third. 

The  third  of  a  chord,  especially  if  it  be  major,  is  particularly 
conspicuous,  and  in  certain  registers  so  overweights  the  chord  that 
little  else  is  heard.      This  is  particularly  true  in  a  low  register. 


Ex.  21 


Doubled  in  a  higher  register  between   soprano  and   alto,   or  alto 
and  tenor,  the  effect  is  often  very  agreeable. 


Ex.   22. 


12 


PRACTICAL    HARMONY. 


As  the  doubling  of  the  tonic,  dominant,  or  sub-dominant  strength- 
ens the  tonality  or  key,  it  is  often  well  to  double  these  notes  when 
they  appear  as  either  the  root,  third,  or  fifth  of  a  chord. 


Tonic  doubled  as    Tonic  doubled  as    Tonic  doubled  as 
root  of  a  chord,      third  of  a  chord.       fifth  of  a  chord. 


Ex.  23. 


\ 


i 


PSJ 


j£2=j- 


-<SM- 


■*L 


] 


-&z 


's 


II 


But  as  a  ride  it   is  best  to  double  the  root  of  a  chord.      Play  and 
note  the  comparative  effects  of  the  following: 


Ex.  24. 


Root  doubled. 


^ 


o 


9* 


i 


-&- 


-<5>- 
-G>- 


-O- 


VFifth  doubled  VThird  doubled. 
Y--V- 


%  - 


-<&- 


—&- 


-O- 


-&>- 


-<s>- 


■& 


fj 


-&- 


--&- 


-<2- 


sr 


o 


-O.- 


:i-! 


II 


The  leading-tone  is  rarely  doubled  unless  belonging  to   a  chord 
formed  on  the  third  degree  of  the  scale  : 


Ex.  25- 


It  sometimes  becomes  necessary  to  omit  one  of  the  notes  oi  a 
chord.  In  elementary  harmony  the  fifth  is  the  only  note  that  may 
be  omitted. 


MELODIC    PROGRESSION. 

The  progression  of  a  voice  from  one  tone  to  another  is  called  a 
melodic  step.  A  sufficient  number  form  a  melody,  air,  or  song. 
The  best  and  really  only  thing  theory  can  do  to  aid  one  to  melodic 
writing  is  to  point  out  progressions  which  are  disagreeable  to  the 
ear  or  difficult  of  intonation. 


PR  AC  TIC  A  L    HA  RMON  Y. 


13 


The  melodic  intervals  permitted  are  :  all  the  major  and  minor  in- 
tervals to  and  inclusive  of  the  minor  sixth,  the  chromatic  interval, 
and  the  octave. 

The  major  sixth,  minor  seventh,  and  all  the  diminished  and  aug- 
mented intervals  are  forbidden,  with  the  exception  of  the  diminished 
fifth  which  is  permitted  when  the  second  note  is  leading-tone, 
moving  up  one  half-step,  as  at  a,  or  the  same  interval  inverted, 
with  the  upper  note  moving  dozen  one  half-step,  as  at  b.  The  two 
are  often  combined,  as  at  c. 


Ex.  26. 


ft. 


-&■ 


-&- 


=t 


-z^- 


-&- 


I 


-&- 


WE*l 


-&- 


J 


-&- 


jQ.- 


I 


The  leading-tone,  so  called  on  account  of  its  strong  melodic  ten- 
dency to  lead  to  the  tonic,  may  move  to  other  degrees  of  the  scale 
under  conditions  like  the  following :  If  the  second  chord  does  not 
contain  the  tonic,  as  at  a,  the  leading-tone  may  skip.  If  the  leading- 
tone  does  not  belong  to  the  chord  of  the  dominant,  as  at  b,  or  if  it 
does  belong  to  the  dominant,  but  is  placed  in  an  intermediate  voice, 
as  at  <?,  it  may  descend. 


Many  popular  hymns  and  patriotic  songs  contain  good  examples 
of  natural,  expressive  melody.  In  the  following  illustrations  it  will 
be  noticed  that  nearly  all  of  the  intervals  are  small,  and  that  they 
progress  mostly  in  the  scale. 


H 


PRACTICAL    HARMONY. 


GOD    SAVE   THE    QUEEN. 


*^-* 


*•  » 


^zzp 


-<2- 


SH 


frF1'-* 


^ 


-^  • 


*=rw 


err?: 


^ 


g^ 


S3E 


AUSTRIAN    HYMN. 


tf 


Spe^fe^ 


»  • 


E^3 


£* 


at±aH4 


s* 


H3 


EM^KxEsEEFE 


£±t 


^E 


p=^=^ 


•-^ 


B=£^F 


£ 


l§5iH 


RUSSIAN    HYMN. 


^: 


^=fpS 


-<s>— £*- 


f=t= 


-«- 


±=rt 


<-^-^-»#- 


l5>- 


^ 


<c^l 


^^ 


V 


•^0 


EE¥ 


r±    = 


?-§!? 


-|2-#- 


£ 


P-^-» 


■&—& 


&— 


DANISH    NATIONAL    HYMN. 


es?^5 


i — 1-#- 


*  * 


-*2-iS»- 


:-^-£- 


^fesfffl 


ttt — i— r-  * 


F 


'  s  i-l —  -I — y-hH — I — hi — I— "-•  * 


t-£± 


i.W 


-*"i 

* 


!E£d3JE£t/:p£: 


o     ?5 


EELt2H^ 


: 


5 


■n 


=& 


F=t=4 


mjlJ—14- 


^B 


xL" 


7P^f-f 


t=£ 


^z— <s> 


R2-* 


II 


THE    WATCH    ON    THE    RHINE. 


i 


— H l^-H— a — 1—4- 


\-<S>-^-0- 


^4=i 


m—m- 


t 


r^m 


=p^ 


->  0^0 


d.d  f  j» 


&-\ 


& 


U 


^  00 


m=^ 


-p-*- 


a 


rRA  C  TIC  A  L    HARMONY. 


15 


It  is  a  mistake  to  think,  as  many  do,  that  all  the  beautiful  melo- 
dies of  the  great  composers  came  to  them  suddenly,  as  inspiration, 
and  that  they  were  written  as  first  conceived  and  never  changed. 
Nearly  all  of  Beethoven's  melodies  are  rhythmical,  simple,  and  nat- 
ural in  intervals  and  modulation,  yet  no  composer  spent  more  time 
in  changing,  polishing,  and  perfecting  his  melodies  than  did  he. 

HARMONIC    PROGRESSION. 

Here,  as  in  the  rules  for  melodic  progression,  all  that  can  be 
done  is  to  point  out  as  clearly  as  possible  those  harmonic  progres- 
sions which  are  repugnant  to  the  ear  and  have  been  avoided  by  all 
the  masters.  If  striking  exceptions  are  found  in  the  works  of  these 
great  composers,  one  may  be  sure  that  these  masters  first  knew  the 
value  of  the  rule  before  they  disregarded  it. 

Those  who  know  most  about  such  matters  agree  that  the  best 
way  to  study  any  form  of  ait  is  by  absorption.  The  student  will 
save  much  time  and  labor  if  he  will  follow  the  advice  of  his  teacher, 
taking  a  great  deal  for  granted.  It  is  not  wise  to  experiment  on 
matters  already  solved  by  others.  He  will  later  fully  appreciate 
and  understand  present  restrictions. 

But  the  teacher  should  explain  as  clearly  as  possible,  and  es- 
peciallv  by  appealing  to  the  musical  instinct,  why  one  progression 
is  forbidden,  another  permitted. 

In  connecting  the  different  triads  in  a  satisfactory  succession, 
either  of  three  movements  may  be  used. 

When  voices  rise  or  fall  simultaneously,  as  at  a,  example  2S,  the 
motion  is  said  to  be  parallel,  or  similar. 

When  one  voice  rises  while  another  falls,  as  at  b,  the  motion  is 
said  to  be  contrary. 

When  one  voice  remains  stationary  while  another  rises  or  falls, 
as  at  c,  the  motion  is  said  to  be  oblique. 


Ex.  28. 


dri^-JrdrdrJ 


1    ^>  I    « 


PS  * 


Contrary  motion  is  preferable  to  cither  oblique  or  parallel.  By 
its  use  the  parts  gain  individuality,  and  many  progressions  which  are 
considered  taultv  are  avoided. 


i6 


PRACTICAL    HARMONY. 
CONSECUTIVE    FIFTHS    AND    OCTAVES. 


If  the  student  will  play  the  following  melody  with  an  added  part 
five  notes  below,  he  will  find  it  most  disagr.eeaLle. 


Ex.  29. 


*->   -*-     •  i  i    i 


d=±b=t 


J 


■ft 


r 


r 


Till    i/i       ^ 


Nor  will  he  find  it  more  acceptable,  but  rather  worse,  if  the  mel- 
ody be  doubled  one  octave  lower. 


Ex.  30. 


S 


9 


—m — m — m — V&  — 


etc. 


Consecutive  fifths  or  octaves  like  the  above,  either  by  parallel  or 
contrary  motion,  are  forbidden. 

Fifths  by  Fifths  by  Octaves  by  Octaves  by 

parallel  motion,  contrary  motion,  parallel  motion,  contrary  motion. 

( S=s^h=^=  =^h=^~  =?-  =i=  =s= 

Ex.  3 


There  are  other  successions  which  taken  alone  are  nearly  as   un- 
satisfactory as  fifths,  as,  for  example,  a  succession  of  fourths: 


Ex.  32. 


^ 


<5>- 


'& 


^ 


-&- 


-&- 


-&■ 


-G>- 

sr 


jO- 


<S>- 


i 


But  the  preceding  may  be  made  very  musical  by  the   addition  of 
another  interval : 


Ex.  33. 


r=2$-- 


jGL- 


rs 


-d- 


& 


-&.- 


-<S>- 


.a.- 


-&- 


-&- 


While  the  bad  effect  of  consecutive  fifths  is  rarely  bettered  by  any 
arrangement  of  the  voices. 

Consecutive  unisons^  either  by  parallel  or  contrary  motion,  are 
forbidden  : 


PRACTICAL   HARMONY. 
Parallel  motion.  Contrary  motion. 


l7 


Ex.  34. 


*> 


re 


-a. 


re 


(2- 


i 


-&- 


m 


-<2- 


-jO.- 


-<S2_ 


ST 


IJ 


THE    TRITONE. 
A  tritone  is  an  interval  of  three  whole  steps. 


Ex.  35. 


I 


m 


~SP' 


-G>~ 


1 


This  succession,  when  heard  under  certain  conditions,  produces 
one  of  the  worst  possible  effects,  and  for  this  reason  was  called  the 
diabolus  in  musica  by  the  old  school  of  Italian  musicians. 

\\  hen  the  chords  of  the  dominant  and  sub-dominant  are  heard  in 
succession,  with  the  leading-tone  in  the  soprano  followed  by  tonic,  the 
two  notes  of  the  tritone  are  heard,  first  in  the  soprano,  then  in  the 
bass. 


Ex.36. 


This  harsh  effect  is  called  the  false  relation  of  the  tritof?e,  and 
should  be  avoided  by  placing  the  leading-tone  in  an  intermediate 
voice. 


Ex.  37. 


SEQUENCE. 

A  sequence  is  a  symmetrica]  repetition  of  a  melodic  or  harmonic 
figure. 


Ex.  38. 


Melodic. 

4— -El 


t"^J\{^..;\.  .:..;!! 


^. 


t$ 


PRACTICAL   HARMONY. 


Harmonic. 


Ex.  39. 


In  the  above  harmonic  sequences  the  same  bass  is  harmonized 
three  ways.  In  each  all  voices  move  regularly  in  exact  sequence. 
But  tin's  is  not  always  necessary,  nor  need  the  responsive  figure 
always  be  exactly  reproduced. 

In  sequence,  the  ear  being  gratified  by  a  regularly  recurring 
rhythmic  figure,  certain  progressions  which  would  otherwise  be 
considered  faulty  are  permissible. 

Note.  It  is  not  expected  that  the  student  will  memorize  or  even 
understand  all  the  rules  and  accompanying  illustrations  in  this  chap- 
ter. They  are  placed  here  more  for  future  reference  than  present 
study,  and  he  will  better  appreciate  them  after  writing  the  succeed- 
ing exercises. 

The  foregoing  illustrations  are  condensed  for  convenient  reference 
into  the  following 

RULES    FOR    HARMONIZING    BASSES. 

MAJOR    MODE. 

I.-  If  no  figure  stands  over  the  first  bass  note,  begin  the  exer- 
cise with  the  octave  of  that  note  in  soprano,  placing  the  other  notes 
of  the  triad  in  the  nearest  position  underneath.  A  3  or  5  signifies 
that  the  soprano  is  to  begin  with  the  interval  indicated.  This  ap- 
plies to  the  first  chord  only. 

II.   If  a  chord  contains  notes  that   were  in  the   preceding  chord, 
they   should  be  retained    in   the    same   voices.      This   rule   may  be 
lisregarded   under  the  following  conditions: 

When  the  bass  moves  from  the  second  note  of  the  scale  to  the 
dominant,  as  at  a ;  when  the  second  chord  is  a  repetition  of  the  pre- 
ceding chord,  as  at  /> ;  and  in  sequence,  as  at  c. 

b. 


Ex.  40. 


-I- 


A~Z 


iz=iiiiz=| 


e 


-&- 


>)■■ 


eI^USS 


PR  A  C  TIC  A  L   HA  RMONY. 


19 


III.  If  there  are  no  notes  alike  in  consecutive  chords,  move  the 
soprano,  alto,  and  tenor  in  contrary  motion  to  the  bass. 

IV.  Consecutive  fifths  and  octaves  are  forbidden. 

V.  Allow  no  voice  to  progress  any  augmented  or  diminished 
interval  except  the  augmented  prime — chromatic  interval —  and  the 
diminished  fifth,  as  in  example  26. 

VI.  In  the  succession  V,  IV,  do  not  allow  the  relation  of  the 
tritone  between  soprano  and  bass.      (  See  examples  36  and  37.) 

VII.  Double  the  leading-tone  rarely  except  in  sequence. 

SUGGESTIONS. 

Choose  positions  neither  too  high  nor  too  low. —  Do  not  pass  the 
limits  in  example  20;  the  extremes  should  be  of  short  duration. — 
As  a  rule,  double  the  root  in  preference  to  any  other  interval. — Con- 
trarv  motion  is  stronger  than  either  parallel  or  oblique. — With  a 
bass  moving  sequentially,  seek  a  corresponding  svmmetrv  in  the 
other  voices. — Although  not  invariably  to  be  observed,  it  is  usually 
best  to  close  an  exercise  with  the  soprano  ending  on  tonic,  pre- 
ceded by  leading-tone. 

Note.  Particular  attention  is  called  to  the  fact  that  when  the 
bass  moves  from  the  second  degree  of  the  scale  up  to  the  dominant, 
it  is  often  best  to  move  the  three  upper  voices  in  contrary  motion 
to  the  bass.  See  first  exception  to  Rule  II.  Also  when  the  bass 
moves  from  the  dominant  to  the  sixth,  it  is  often  best  to  double 
the  third  of  the  chord  on  the  sixth  degree.  This  is  especially  true 
if  the  chord  on  the  dominant  has  its  third  —  leading-rone  —  in 
soprano. 


Not. 


Ex.  41. 


% 


-72- 


-TOT 


-1& 


& 


-& 


-&- 


II 


II 


A  careful  observance  of  the  preceding  suggestions  will  save  the 
student  much  labor  and  needless  confusion  when  he  comes  to  exer- 
cises in  the  minor  mode. 

In  the  following  exercises  a  soprano,  alto,  and  tenor  are  tc  be 
added  to  the  given  bass,  according  to  foregoing  rules.  In  harmo- 
nizing these  basses  no  instrument  should  be  used.  The  key- 
board should  not  be  touched  until  the  exercises  are  finished. 


20 


PRACTICAL   HARMONY. 


A>. 


1. 


2. 


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PR  A  C  TIC  A  L    HA  RMONY. 


21 


After  these  basses  have  been  harmonized  they  should  be  played ; 

whenever  a  succession  is  unsatisfactory  it  is  possible  that  a  rule  has 
been  violated.  If  a  passage  could  be  written  in  either  of  two  ways, 
each  apparently  correct,  write  the  form  preferred  in  large  notes, 
and  the  other  possible  disposition  in  small  notes.  After  the  exer- 
cises have  been  corrected  in  this  way  by  the  student,  with  the  aid 
of  an  instrument,  he  should  listen  to  them  while  played  bv  another. 

Without  looking  either  at  the  keyboard  or  the  music  he  should 
name  the  major —  principal — triads  whenever  they  occur.  As  soon 
as  these  can  be  readily  distinguished  the  minor  chords  should  be 
named  in  like  manner.  This  exercise  stimulates  the  musical  in- 
stinct and  should  be  followed  throughout  the  book. 

It  is  recommended  that  the  preceding  exercises  be  corrected  be- 
fore the  following  additional  basses  are  harmonized.  The  lessons 
should  all  be  written  in  ink,  and  the  pupil  should  come  to  his  les- 
son prepared  to  play  them  in  the  key  in  which  they  are  written, 
and  also  to  transpose  and  play  them  in  the  keys  indicated  by  a 
capital  letter  at  the  right  of  each  bass.  This  practice  of  transposing 
the  lessons  should  be  continued  in  keys  selected  by  the  teacher. 


ADDITIONAL    EXERCISES. 

The  following  basses  are  to  be  harmonized  according  to  previous 
rules.  The  repetition  of  notes,  irregular  rhythms,  and  generally 
light  character  of  these  exercises  are  purposely  introduced  ;  it  is  one 
one  of  the  aims  of  this  book  to  lead  the  student  bevond  the  writinsr 
of  monotonous  psalm-tunes.  Although  the  succeeding  exercises  are 
instrumental  rather  than  vocal,  all  previous  rules  regarding  the  tieing 
over  of  notes  common  to  consecutive  chords  should  be  strictly  fol- 
lowed. Whenever  rests  occur,  as  in  exercise  5,  the  voices  should 
move  to  the  next  chord  in  as  strict  accordance  to  rule  as  though  there 
were  no  rests.  As  a  general  thing  it  is  best  to  tie  over  a  note 
which  will  bring  contrary  motion ;  this  rule  may  often  be  disre- 
garded in  progressions  like  the  following,  when  the  outside  voices 
move  in  thirds. 


Ex.  42. 


I 


% 


J 


i 


o 


¥ 


1  i 


I 


" 


V 


!! 


22 


PR  AC  TIC  A  L   HA  RAW  A  Y. 
EXERCISES. 


Allegretto. 

8 


1. 


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II 


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1 


Andante. 


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Lightly. 

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PR  A  C  TIC  A  L   HA  RMONY. 


23 


CHAPTER    III. 

SCALES. 

THE    MINOR    MODE.     MELODIC    AND    HARMONIC     PROGRESSIONS    IN    THE    MINOR 
MODE.     THE    AUGMENTED    SECOND. 

The  two  scales  employed  in  modern  music  are  the  major  and 
minor. 

Each  major  scale  has  an  accompanying  or  related  minor  scale, 
called  its  relative  minor. 

It  is  customary  to  use  capital  letters  in  designating  the  major  keys  ; 
small  letters  the  minor. 


Ex.  43. 


C  (Major).         a  (Minor). 


The  relative  minor  of  any  major  scale  has  for  its  starting-point, 
or  tonic,  the  third  note  of  the  descending  major  scale,  and  its  sig- 
nature is  the  same  as  the  major  to  which  it  is  so  closely  related. 

The  relative  minor  of  C  would  be  a  ;  that  of  G,  e  ;  and  that  of  F,  d. 

A  major  and  its  relative  minor  are  said  to  be  related,  because 
they  look  and  sound  much  alike. 

The  major  scale  of  C  is  formed  as  at  I.  in  example  4-4  i  one  of  the 
earliest  forms  of  its  relative  minor,  a,  stood  as  at  II. : 


II. 


Ex.  44. 


* 


3=± 


P^ 


:«=; 


I 


This  form  was  in  use  long  before  our  major  scale.  It  has  under- 
gone various  transformations,  which  would  here  be  confusing  and 
valueless.  The  form  used  to-day  in  elementary  harmony,  and  for 
that  reason  called  the  harmonic  minor  scale,  stands  as  at  II.  in  the 
preceding  example,  with  its  seventh  note  chromatically  raised. 


Harmonic  Minor  Scale  of  a. 


Ex 


.'45.fi 


1=4 


-tr    ~* 


ill 


24 


PR  AC  TIC  A  L   HA  RMONY. 


The  harmonic  minor  scale,  then,  is  found  by  taking  the  third  note 
of  the  descending  major  scale  for  a  tonic,  and  chromatically  raising 
its  seventh  note. 

This  seventh  was  raised  to  gain  a  leading-tone  and  to  secure  a 
dominant  chord  in  minor  the  same  as  in  major.  A  chord  on  the 
fifth  degree  in  any  minor  key  without  this  leading-tone  would  be  dis- 
appointing and  produce  no  satisfying  clocr. 


Ex.  46. 


I 


-<9- 


-<s- 


-25*- 


% 


==1= 


=^=f 


^\ 


— <&- 


53-- 


-Z51- 


— <&- 


II 


* 


-^ 


-£*- 


^B 


At  a,  the  closing  chords  are  vague  and  unfinished ;  at  6,  the  same 
chords  with  the  seventh  raised  give  a  satisfying  close. 

In  the  major  scale,  example  44,  the  half-steps  come  between  the 
third  and  fourth,  and  seventh  and  eighth  degrees.  In  the  minor 
scale  the  order  is  quite  different,  and  it  is  this  different  disposition  of 
intervals  which  gives  to  each  scale  its  character. 


Ex.  47. 


A 


*--* 


§i 


It  will  be  noticed  that  there  are  three  half-steps  in  the  minor  scale. 

Between  the  sixth  and  seventh  degrees  of  the  minor  scale  there 
occurs  the  interval  of  an  augmented  second.      See  X  in  example  47. 

This  interval  does  not  occur  in  the  major  scale,  and  following  the 
general  rule  that  no  augmented  intervals  are  to  be  written,  this  aug- 
mented second  must  not  be  used  in  elementary  harmony. 

In  the  rules  for  harmonizing  basses  in  the  major  mode,  the  rule  for 
retaining  notes  in  the  same  voice  could  be  disregarded  when  the  bass 
moved  from  the  second  degree  to  the  fifth.  It  is  necessary  to  do  this 
when  the  succession  comes  in  the  minor  key,  in  order  to  avoid  the 


augmented  second. 


I 


Augmented  second. 


^s 


"V 


Ex   48. 


( 


): 


-jO.. 


— I- 


■& 


* 


22- 

J (9. 


> 


I 
1 


II 


PRACTICAL   HARMONY. 


In  the  major  mode  it  is  often  well  to  double  the  third  on  the  sixth 
degree.  In  the  minor  mode  the  third  on  the  sixth  degree  must  al- 
ways be  doubled  when  preceded  by  the  fifth  degree,  to  avoid  the 
augmented  second. 


Ex.  49. 


V  VI  V         VI  V  VI 

The  third  doubled  in  the  octave,  as  at  a  in  preceding  example,  is 
always  preferable  to  the  unison,  as  at  b.  This  unison  between  soprano 
and  alto  weakens  the  harmony,  and  should  not  be  used  when  another 
disposition  is  possible,  unless  coming  on  an  unaccented  part  of  a 
measure,  as  at  a  in  following  example,  or  at  the  close  of  a  musical 
phrase,  as  at  b.  Even  in  the  latter  it  is  generally  better  to  allow 
the  leading-tone  to  descend,  as  at  c,  in  order  to  gain  a  full  chord  at 
the  close. 

a.  b.  c. 


Ex.  50, 


1 


m 


3 


i 


~83T~arfH 


S& 


m 


cc 


-gf>- 


-&- 


& 


£2_ 


II 


-G.- 


Cf 


& 


a.- 


-!S>- 


II 


The  unison  is  least  objectionable  between  inside  voices,  and  is  best 
introduced  on  the  weak  part  of  the  measure. 

The  different  kinds  of  triads  in  the  minor  mode  are  as  follows: 


Minor, 


Dim. 


Aug.         Minor.     Major.     Major.     Dim. 


Ex.  51 . 


I 

-3- 


i 


_ 

11° 


iikS 


3 


g 


19 
III* 


"SP- 


IV 


19 


m 


*> 


s> 


-<52—  -n3- 

-62 SS 

^^ r    w^ 


VI 


VII' 


For  the  present  the  diminished  chord  on  the  leading-tone,  and  the 
augmented  triad  on  the  third  degree  will  not  be  used.  Reasons  for 
this  will  begiven  later.  The  diminished  triad  on  the  second  degree 
will  be  of  frequent  use.  The  principal  chords  oi  the  minor  mode  are 
the  same  as  those  of  the  major,  and  all  that  is  written  regarding 
them  there  is  equally  applicable  here. 


36 


PRACTICAL    HARMONY. 


Whenever  a  sharp,  flat,  or  natural,  stands  over  a  bass  note  -with- 
out a  figure  by  its  side,  as  at  a,  example  52,  it  signifies  that  the 
third  note  from  the  bass  is  to  be  chromatically  changed.  A  figure 
by  the  side  of  a  chromatic  sign  calls  for  the  corresponding  interval 
from  its  bass  to  be  altered.      See  />. 


Ex.  52. 


A  chromatic  sign  once  used  to  change  a  note,  will  effect  all  other 
notes  in  that  measure  that  are  on  the  same  degree. 

ADDITIONAL    RULES    FOR    HARMONIZING    BASSES. 

MINOR    MODE. 

I.  Whenever  the  bass  moves  from  the  fifth  to  the  sixth  degree  of 
the  scale,  or  vice  versa,  double  the  third  of  the  chord  on  the  sixth 
degree. 

II.  Whenever  the  bass  moves  from  the  second  degree  of  the  scale 
up  to  the  fifth  degree,  move  the  three  upper  voices  in  contrary  motion. 

Xotc.  The  early  musicians,  as  a  rule,  made  the  final  chord  of 
any  piece  of  music  major,  even  though  the  mode  were  minor. 
Such  concluding  chords  should  not  be  looked  upon  as  changes  of 
key  or  modulations,  hut  rather  as  a  change  otform  from  the  minor 
triad  to  the  major. 


PAL7.STRINA. 


Ex.  53. 


\J   " 

"" 

f  ^     £ 

1^— 

9V  5  - 

-v  1 

• 

1     " 

m 

^—] 

^  5     * 

&— 

— - — H 

These  early  writers  looked  upon  the  minor  third  in  a  triad  as  an 
imperfect  or  artificial  interval,  and  consequently  rarely  used  it  in 
a  concluding  chord.  This  concluding  optional  major  third  will  oc- 
casionally be  found  in  the  succeeding  exercises  ;  it  will  be  designated 
by  the  necessary  sharp  or  flat  enclosed  in  parenthesis,  as  in  examples 
2  and  3  in  Additional  Exercises. 


PRACTICAL   HARMONY. 


*7 


SUGGESTIONS. 

Carefully  reread  the  rules  and  accompanying  Suggestions  at 
close  of  Chapter  II.  The  student  will  do  well  to  look  the  basses 
through  before  harmonizing  them,  noting  those  places  where  the 
bass  moves  either  from  V  to  VI,  or  VI  to  V,  or  from  n  to  V. 
After  marking  the  places  where  these  successions  occur,  again  read 
the  two  additional  rules  for  harmonizing  basses  in  the  minor  mode. 


■&- 


EXERCISES. 


G>- 


i 


l. 


§3 


4-z? 


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*> 


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2-  EiSs 


HE=rr=^ 


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jS.- 


3. 


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f. 


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4.   zgifcrffigEgzi 


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4 


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D 


7. 


8. 


F 


F—f 


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II 


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1   1. 


PRACTICAL   HARMONY. 

a    -s>-.  b     „. 


SSfeS 


$££*=£: 


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ADDITIONAL    EXERCISES. 
The  following  exercises,  corresponding  to  the  Additional  Exercises 
in  Chapter  II.,  should  be  harmonized  after  the  preceding  exercises 
have  been  corrected. 


1. 


o   :  B  B  •-  0  B  B 


a    t 


2-  E§3fe*fe^EpEf 


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II 


EXERCISES. 


The  student  should  now  compose  several  short  basses  in  both  the 
major  and  minor  modes.  The  arrangement  of  all  like  work  must 
be  left  to  the  discretion  of  the  teacher.  This  original  work  is  of 
the  greatest  importance,  and  should  be  insisted  on  at  each  lessor. 


r/iA  C  J  JCA  L   II A  KMONX. 


** 


CHAPTER   IV. 

CHORD   RELATION.     HARMONIZING     MELODIES 

The  relative  good  or  bad  effect  of  a  chord  depends  much  upor 
preceding  and  succeeding  chords.  The  same  chord,  placed  undei 
different  conditions,  produces  wholly  opposite  effects.  This  is  st 
true  that  a  triad  heard  under  changed  conditions  so  changes  in  char- 
acter, that  to  the  inexperienced  ear  it  is  unrecognizable.  A  chore 
which,  preceded  by  certain  other  chords  sounds  very  disagreeable, 
may  become  under  other  conditions  one  of  the  most  agreeable.  The 
truth  of  this  may  be  in  a  measure  realized  by  playing  the  following 
illustrations,  which  contain  precisely  the  same  chords : 


Ex.  54. 


19- 


HiB 


Sir 


II 


m 


§fc§ 


I 


-&- 


V- 


1 £>- 


r> 


II 


That  at  a  is  almost  intolerable,  while  that  at  b  is  acceptable. 

The  chord  on  the  leading-tone,  marked  x,  is  unpleasant  at  the 
1  ?st  when  coming  in  the  major  key  with  its  root  doubled,  and  for 
that  reason  has  not  been  used.  This  same  chord  in  the  minor  mode 
is  full  of  character  and  beauty. 


Ex.  55. 


3° 


PRACTICAL    HARMONY. 


When  one  hears  an  isolated  consonant  chord,  the  ear  immedi- 
ately accepts  it  as  a  tonic.  If  there  are  several  chords  in  succession 
the  ear  is  not  satisfied  until  the  tonic  is  again  heard. 


Ex.  56. 


At  a,  example  56,  there  is  no  satisfactory  close  ;  at  fr,  the  same  suc- 
cession with  the  tonic  added  is  complete  and  satisfies  the  ear.  For 
this  reason  it  is  generally  best  to  begin  and  close  a  piece  of  music 
with  the  chord  of  the  tonic. 

In  a  series  of  chords  there  are  three  chords  which  must  be  more 
frequently  heard  than  others  in  order  to  make  the  tonality  and  mode 
decisive.  These  are  the  tonic,  dominant,  and  sub-dominant.  A  suc- 
cession which  did  not  contain  more  of  these  principal  triads  than 
the  secondary  triads,  would  be  indecisive  and  lack  tonal  force. 
Their  excessive  use  produces  monotony  ;  their  good  effect  is  height- 
ened bv  the  judicious  intermixture  of  chords  on  the  other  degrees. 
Composers  give  as  delicate  attention  to  chord-succession  as  paint- 
ers do  to  the  mixing  of  colors. 

The  chords  of  the  tonic,  dominant,  and  sub-dominant  have  the 
strongest  tonal  force ;  next  to  these  in  tonal  force  are  the  chords 
formed  on  the  sixth  and  second  degrees ;  the  latter  should  neither 
be  too  frequent  nor  too  prolonged.  The  chord  on  the  third  degree 
in  the  major  mode  is  weak,  tonally,  and  should  be  more  rarely  in- 
troduced. The  augmented  triad  on  the  third  degree  of  the  minor 
mode,  as  well  as  the  diminished  on  the  leading-tone  of  either  mode, 
are  not  to  be  used. 


HARMONIZING    MELODIES. 
THE    MAJOR    MODE. 

In  the  following  exercises  a  soprano  is  given,  to  which  alto,  tenor, 
and  bass  are  to  be  added. 

The  rules  given  for  chord  progression  in  the  harmonizing  of  basses 
apply  here.     A  soprano  note  could  be  harmonized  as  either  the  root, 


rRA  C T1CAL   HA  RMONY 


3* 


third,  or  fifth  of  a  chord.      For  example,  C  could  be  either  the  root 
of  a  chord,  as  at  a,  the  third  of  a  chord,  as  at  6,  or  the  fifth,  as  at  c. 


Ex.  57. 


b. 


~Z7- 


-&- 


-G>- 


~or 


-&- 


. — &- 


&- 


1:1 


0 


SUGGESTIONS. 

Besrin  each  exercise  with  tonic  and  close  with  same. — The  inter- 
vening  chords  should  consist  largely  of  the  three  principal  triads. — . 
The  chords  on  the  second  and  sixth  are  of  frequent  occurrence. — 
The  chord  on  the  third  degree  should  rarely  be  used  except  when 
followed  either  by  the  sub-dominant  or  the  sixth. 


Ex.  58. 


A 

r- 

— V 

/" 

^N 

u 

yr       ^ 

e>   - 

f\        & 

& 

Z? 

II 

w 

■ft 

~& 

Zr 

-&- 

m 


--&- 


-ts>- 


I — &- 


z? 


1 


A  chord  maybe  built  on  any  note  of  the  scale  except  the  leading- 
tone. —  It  will  be  found  best  to  first  compose  a  bass,  then  add  the  in- 
termediate parts. —  The  harmony  should  change  with  each  soprano 
note,  and  the  root  of  each  chord  must  be  in  the  bass. —  Never  move 
from  the  fourth  degree  to  the  third  degree. —  (See  note  Ex.  59.) 
Never  move  from  the  fifth  degree  to  the  fourth  degree,  with  the 
soprano  moving  from  leading-tone  to  tonic. 

Note.  The  progression  from  the  fourth  degree  to  the  third  degree 
produces  the  false  relation  of  the  tritone. 


Ex.  59. 


r#~ 

II 

w 

II 

■ 

tr      ^. 

^ 

—&— 

O 

1 

32 


PRACTICAL   HARMONY. 


Note.  When  first  attempted,  the  harmonizing  of  melodies  is 
exceedingly  difficult.  The  following  exercises  should  bere  written 
till  satisfactory  to  the  teacher.  With  the  average  pupil,  two  or 
three  or  perhaps  more  lessons  should  be  spent  on  this  chapter. 
Not  more  than  eight  melodies  should  be  harmonized  before  the 
teacher  corrects  them.  The  practice  of  transposing  should  be  con 
tinued. 


1. 


MELODIES. 

THE    MAJOR    MODE. 


er^t 


r> 


d: 


•rizfci 


-s>- 


0^  0-0 


B. 


8 


2.  =7f:  (T^= 


g 


■&—&- 


■f^-e- 


I 


3. 


-*mm 


:i 


E^. 


-•>  d  •- 


■73- 


0—0- 


*$=$=*$=* 


0       • 


4. 


atS 


H~ 


i 


•  * 


tri 


e 


£ 


±*g£ts!: 


si 


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F 


0000 


*=± 


II 


It 


«-*+*•!     *      J-J=+ 


-<&— 


6. 


ITl^     ■ 


0^-0-0    0 


^4 


d=p=tr=|: 


*b. 


FffM4^MI 


A  -    *  G. 

Fffi^S3jrT=tJT::l=^ 


7. 


8. 


»^^ 


d    \d.     +■ 


j: 


#b. 


-(=- 


1 


PR  A  C  TIC  A  L   HA  KMONY. 


33 


9. 


fc^^ 


m 


fr-fr^1!     f   |     F 


j22_ 


-P=  #- 


t5> — 


*— m—  • 


fe^l 


10. 


tet 


«g 


-& — «> 


-I— MM 


-f52— «>- 


>5 


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P—<9- 


I 


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eV 

=?w^r* 

.  £? 

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& 

~- — H 

1(1 ) — ^  P  V 

— s> — 

a 

' — <s> — 

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12 


zta=«=4 


iSbtfc*: 


— «»— 


* — *- 


4 — 1-4 


-z?- 


II 


i= 


13. 


14. 


15. 


^E 


-&- 


»   # 


F 


-«a_ 


-<s>- 


M= 


II 


S 


A\>. 


£%£=£ 


t—m—t 


M=t=c 


^-= — 


<&- 


1 


tf H  '         ' 


?=g= 


-<S>- 


"Z?" 


-<©— 


Gt>. 


25 


II 


MELODIES. 
THE    MINOR    MODE. 


I 


m 


-* — * 


%&-* 


m — * — # 


.$* 


-25*- 


i 


g^ 


2. 


II 


=fc 


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e).        J. 


© 


(»)2= 


3-    :^ 


^ 


z^8. 


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^ 


\> 


l 


u 


4. 


feI££H*»: 


:S3 


c-> 


(O      -> 


o 


&* 


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34 


PRACTICAL   HARMONY. 


5. 


to 


iWEStg 


tad 


ft- 


•Td— d — !- 


•jj£ 


&s>- 


=t 


-g^-gH-g* 


!  Jl     1=H 


--^^ 


(5) 


ife^pgi^^^^ 


?d==H 


CHAPTER  V 


FIGURING    OF   THE    BASS. 


OPEN    HARMONY. 


In  order  to  indicate  as  clearly  as  possible  the  position  which  the 
notes  forming  a  harmony  are  to  occupy,  figures  are  placed  either 
above  or  below  the  bass. 

The  figures  indicate  the  relative  position  of  the  upper  three  voices 
above  the  bass.  The  figures  |  would  signify  that  an  octave  of  the 
bass  should  be  in  the  soprano,  a  fifth  from  the  bass  should  be  in  the 
alto,  and  a  third  from  the  bass  should  be  in  the  tenor.  (See  a, 
example  6o.)  It  must  be  understood  that  these  three  upper  voices 
may  occupy  any  octave  above  the  bass,  provided  the  voices  do  not 
pass  the  limits  given  in  Chapter  II.  The  figures  f  would  signify  that 
a  third  from  the  bass  should  be  in  the  soprano,"  a  fifth  from  the  bass 
in  the  alto,  and  an  octave  from  the  bass  in  the  tenor.      (See  b.) 


Ex.  60. 


^ 


-<2- 


-<S>- 

8 


j2- 


b. 


JO- 


-G>- 


-G>- 

3 
5 

8 


fl 


II 


It  is  often  desirable  to  move  one  voice  of  a  chord  while  the  others 
remain  stationary.  This  may  be  indicated  by  changing  the  figures 
according  to  the  interval  desired,  and  by  drawing  a  horizontal  line 
after  those  figures,  the  corresponding  notes  of  which  are  to  remain 
stationary. 


PRACTICAL   HAKMOXY. 


35 


Ex.61 


a.     |        . 

rfr^r* — — n 

1 1 — i h 

C. 

( 

&£ sJ~+- 

1 — 

-g :  1  g : 

^ 

1 

IMJ  Z    r2                    & 

s?  •     &  ' 

3           8         5 
3 

-<&-.         3          5 

8           

5          3 

J.            1 

■             UP 

5             3       

5              3              5         8              5           8 
1         8                                       3        

1                               ,                       8         

J 

~         Of 

f 

Bi3— = 

-<G>— 

-<s>- 



P*       H 

1 

S    n  a  • 

s>  • 

« •      i « •      ii 

V 

£ 

1          ii 

Such  changes  are  often  made  to  gain  rhythmic  or  melodic  variety, 
or  both.  A  horizontal  line  over  different  bass  notes  signifies  that 
the  harmony  over  the  first  bass  note  is  to  be  continued.  In  such  a  case 
the  upper  three  notes  may  remain  stationary,  as  at  a  in  the  following 
illustration,  or  the  position  —  not  the  harmony  —  may  be  changed, 
as  at  b. 


Ex.  62. 


± 


:± 


:=!: 


m 


A  horizontal   line  drawn  through  a  figure  signifies  that  the  cor- 
responding interval  should  be  diminished. 


Ex.  63. 


-TO- 


:i=h 


^m 


Consecutive  octaves  and  fifths  which  result  from  a  change  of  posi- 
tion of  a  chord,  are  permissible. 


Ex.  64. 


36 


PRACTICAL    HARMONY. 


It  often  occurs  that  a  change  of  position  does   not  correct  what 
would  otherwise  be  consecutive  octaves  or  fifths. 


Ex.  65. 


The  consecutive  octaves  at  a  and  c  are  hardly  more  disagreeable 
than  those  at  b  and  d.  The  change  of  position,  coming  on  the  weak 
part  of  the  measure,  does  not  destroy  the  effect  of  the  octaves.  The 
same  is  relatively  true  of  the  fifths  at  e  andjf,  and  of  the  octaves  and 
fifths  at  g  and  h. 

Experience  and  instinct  are  the  best  guides  regarding  progressions 
like  the  preceding,  because  the  part  of  measure  on  which  the  chord 
occurs,  as  well  as  the  relative  length  of  the  different  positions, 
greatly  influence  the  character  of  the  successions. 


OPEN    HARMONY. 

When  the  soprano,  alto,  and  tenor  lie  close  together,  as  at  a, 
example  66,  the  harmony  is  said  to  be  in  close  position. 

When  the  voices  are  so  disposed  that  the  soprano,  transposed 
one  octave  lower,  comes  between  the  alto  and  tenor,  or  the  tenor, 
placed  one  octave  higher,  comes  between  the  soprano  and  alto,  as  at 
b,  the  harmony  is  said  to  be  in  open  position  or  open  harmony. 

a.  b. 


Ex.  66. 


- — &- 


-J5L- 


-fi. 


^> 


— a~ 


-O.. 


.£2.- 


-<S>— h 


-G>- 


-<S2- 


-Q- 


JSL. 


j2. 


-<Z- 


-(2- 


II 


It  is  not  as  difficult  to  write  close  harmony  as  open  harmony,  and 
for  that  reason  the  preceding  exercises  were  written  in  close  har- 
mony. 


F/tA  C  TIC  A  L   HA  RMOA  Y. 


37 


Open  harmony  is  generally  much  more  sonorous  than  close  har- 
mony. It  often  occurs  that  in  the  latter  the  alto  and  tenor  voices  are 
too  high,  or  that  too  great  a  distance  separates  the  tenor  from  the 
bass. 

b.        s— 


Ex.  67. 


-<s>— 


=*  9 


4- 


6k- 


-f~ 


-<9- 


±^* 


:i|— S1- 


-«>  — 


-GL—\  -iZ- 


T 


-■&- 


-X 


&h-e\- 


* 


N 

-I        *,    r<g- 


~M: 


-> 


-<9-   -&- 


■^ 


-<S> 


-*9- 


1-&- 


r 


n=2- 


-(S1- 


-S>- 


:£: 


r 


I 


The  two  examples  above  contain  the  same  harmony ;  the  one  at 
b  is  much  the  richer,  and  the  alto  and  tenor  voices  lie  more  in  their 
normal  positions. 

In  the  following  exercises  the  position  of  the  voices  in  the  first 
chord  is  indicated.  After  the  first  chord  the  voices  should  move 
to  the  nearest  position  of  the  next  chord,  according  to  previous 
rules. 

it  often  occurs  that  an  exercise  beginning  in  open  harmony  win 
end  in  close  harmony,  and  vice  versa. 

In  many  of  the  following  exercises  the  second  and  sometimes  the 
third  note  under  which  a  horizontal  line  is  drawn,  is  a  note  foreign 
to  the  harmonv. 


Ex.  68, 


1 
\ 


-&- 


<9- 


-&- 


jO- 


I 


Se|e£ 


-s>- 


3 


2 


.G-±- 


A. 


-f&- 


^ 


-&- 


\ 


All  notes  foreign  to  the  harmony  are  called  "  ■passing-notes;'* 
they  must  be  approached  and  left  diatonically,  i.e.,  they  must 
never  be  skipped  to  or  from.  But  if  the  note  or  notes  belong  to  the 
harmony,  they  may  be  approached  or  left  by  a  skip. 

~\ 1- 


Ex.  69. 


IS 


jO.- 


o> 


m=k 


& 


*=}-- 


ii 


4  0  $  "5°> 


3§ 


PRACTICAL    HARMONY. 


Passing-notes  may  be  employed  in  the  different  voices,  if  by  so 
doing  rhythmical  or  melodic  interest  is  gained.  The  following  frag- 
ment: 


70. 


9. — 0 


would  be  correct,  harmonized  as  follows : 


But  it  would  be  more  interesting  with  passing-notes,  either  in  the 
tenor : 


I 


«== 


&  -0-  -&-. 


atzt 


f^i=f 


r 


-<SJ- 


or  in  the  alto  : 


%-A 


1 


* — • 


j 


ffX-r 


Z-T 


O 


-m— F 1- 


^ 


PRACTICAL   HARMONY. 


i9 


EXERCISES. 


■•IIIeSI 


45SE 


J2-- 


3 
5 

8 


:fS 


5 


rtr 


-H2-- 


5- 

8 
:f 


2.PEJ 


II 


Zz±7t* 


-0T 


~<&-P-^S>- 


-&- 


o   ^ 


^5-^=2- 


75H-- 


■g?— » 


3. 


IWf^ 


■*-*- 


3=E 


vS>— 


r^ 


g=^ 


=j 


*£t* 


[I 


8  5  3 
3  —  8 
5 


4.  iBzdtti-^i 


H=fe 


3  8 
8  5 
5  3 


-&- 


p=r=^ 


S3 


J*** 


£=* 


;^— •- 


i 


5.  i^z-fc^tozj^z^: 
-— P-b-4^  *  |T- 


CHAPTER  VI. 

CHORDS. 
THE    FIRST    INVERSION. 

Many  of  the  preceding  exercises  have  necessarily  been  more  or 
less  dry  and  uninteresting  on  account  of  the  chords  all  standing  in 
what  is  called  their  fundamental  position. 

When  the  root  of  a  chord  is  in  the  bass,  the  chord  is  said  to  be  in 
its  fundamental  position. 

When  any  note  not  the  root  of  a  chord  is  in  the  bass,  the  chord 
is  said  to  be  inverted. 

When  the  third  of  a  chord  is  in  the  bass,  the  chord  stands  in 
what  is  called  its  first  inversion. 


d-O 


PR  A  C  TIC  A  L    HA  RMON  Y. 


At  a  in  the  following  example,  the  chord  is  in  its  fundamental 
position  ;   at  b,  the  same  chord  is  in  its  first  inversion. 

b. 


Ex. 


9- 


^ 


At  b  in  the  preceding  example,  there  is  a  figure  6  over  the  bass 
note.  This  shows  that  the  root  of  the  chord,  C,  stands  above 
the  bass  note. 

Whenever  a  6  stands  over  a  bass  note  it  signifies  that  this  note  is 
the  third  of  a  chord  ;  the  chord  of  which  this  bass  note  is  the  third 
should  be  written. 

If  a  C  were  given  with  a  6  over  it  the  chord  of  A  would  be 
required  ;   a  6  over  F  would  call  for  the  chord  of  D,  etc. 

All  that  was  written  regarding  the  doubling  of  the  third  in  Chap- 
ter II.  should  now  be  reread  ;    it  is  particularly  applicable  here. 

Whenever  the  third  is  in  an  outside  voice  —  soprano  or  bass  — 
it  is  more  prominent  than  when  in  an  inside  voice.  For  this  reason 
it  should  rarely  appear  in  soprano  and  bass  at  the  same  time. 

At  a  in  example  J2,  the  third  coming  in  outside  parts  is  so  strong 
that  little  else  is  heard.  Occasionally,  in  order  to  gain  a  better 
melody  or  rhythm,  the  third  may  be  doubled  in  outside  parts,  as  at 
b  or  c.  At  the  second  measure  of  the  example  at  <~,  the  third  is 
best  doubled.  As  was  explained  in  Chapter  II.,  it  is  often  well  to 
double  the  third  when  it  is  one  of  the  principal  notes  of  the  scale. 


!x.  72. 


The  first  inversion  of  a  chord  is  so  soft  and  pleasing  that  many 
progressions  which  are  harsh  and  disagreeable  in  their  fundamental 
position  become  wholly  satisfactory  when  in  this  first  inversion. 

It  was  for  this  reason  that  the  study  of  triads  in  the  root  position, 
was  made  as  exhaustive  and  exacting  as  possible.      If  the  preceding 


PRACTICAL   HARMONY. 


4-1 


exercises  were  so  arefully  written  as  to  be  to  a  degree  satisfactory, 
it  will  now  be  possible  to  gain  far  more  agreeable  results  with  the 
use  of  the  first  inversion.  This  is  an  important  point  to  keep  in 
mind  when  harmonizing  melodies. 

Parallel  motion,  even  in  four  voices,  is  often  possible  when  mov- 
ing to  a  first  inversion. 


Ex.  73. 


I 


i 


OBSERVATIONS. 

In  chords  of  the  sixth,  as  in  chords  in  the  fundamental  position, 
it  is  usually  best  to  double  the  root —  The  third  may  be  doubled  if 
it  is  one  of  the  principal  notes  of  the  scale,  or  to  gain  a  more  melo- 
dious leading  of  the  parts.  —  In  successive  chords  of  the  sixth,  with 
the  bass  moving  diatonically,  the  third  may  be  doubled  in  alternate 
chords. 

The  diminished  triad  on  the  second  degree  of  the  minor  scale 
usually  appears  as  a  chord  of  the  sixth  with  the  third  doubled. 

Consecutive  fifths  are  permitted  between  inside  voices  if  the 
second  fifth  is  diminished. 


Ex.  74. 


PS 


-&■ 49- 


6   *-i 


& 


r 


(2 


Jg: 


i 


^ 


II 


6  6  6 


(2- 


. 


3 


&         1 


<> 


■-&■ 


II 


1 


%Ep    " 


6  6,, 

-r>5 -=—r-&     & 


i'PP 


o> 


6 ,      6         _ 


-w 


42 


PRACTICAL   HARMONY. 


3.  : 


m 


-G>- 


&- 


6 


tf 


-«>- 


g^jg^^^g|a^^^3i^[| 


5. 


» 


:tfct 


3 


fcfc 


F^i 


X=- 


6 


6  6 


t 


3Edw& 


-•-(- 


*M: 


SpT 


^M\ 


.SEE 


6  6 


6  6 


_(2- 


4= 


-«>— 


±4= 


^i 


A 


H 


-•-•- 


o 


^ 


I 


.Stftf  note. 


65 


7. 


£»£££ 


4=ti 


i9- 


:t==l 


P 


6       65      6       6       65 


^2- 


-(^ 


m 


3      — 

5        # 

8       — * 


s.  ESStefe 


9-B|g^ 


:^ 


-f=2- 


±±zz= 


-<2- 


J] 


10. 


I      * 

8    6 


3» 


:p: 


36    f 


e 


36     J 


3 


F^W 


i 


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d 


e  56« 


s» 


Sit 


B 


Note  to  the  teacher.  If  the  preceding  lessons  have  been  thoroughly 
mastered,  it  is  very  desirabre  that  the  pupil  should  begin  the  study 
of  strict  counterpoint.  If  undertaken  at  this  period  the  student  will 
use  all  the  music  material  he  has  acquired,  and  the  study  will  prove 
less  irksome  than  it  would  later  on,  when  he  would  find  it  neces- 
sary to  begin  again,  and  with  irritating  and  apparently  senseless 
restrictions.  Harmony  and  counterpoint  are  not  different  studies 
but  different  departments  of  one  great  study;  the  former  treats 
more  specifically  of  the  structure  of  chords,  the  latter  of  melodic 
invention.  Nothing  will  so  speedily  give  the  student  an  accurate 
working-knowledge  of  triads,  in  their  root  position  and  first  inver- 


Note.  63,  65,  56,  01^6,  signify  that  two  chords  are  to  be  written  over  one  bass  note.  The 
6  stands  for  first  inversi^  the  other  figure  for  root  position.  In  such  a  case  the  3d  ( the  bass 
note  )  is  usually  doubled  fft  the  6th  chord. 


PRACTICAL   HARMONY. 


43 


sion,  as  the  study  of  strict  counterpoint.  There  is  no  reason  why 
it  should  not  be  taken  up  now,  and  be  carried  on  hand  in  hand 
with  harmony.  It  would  be  preferable  in  conjunction  with  this 
text-book,  to  use  the  treatise  on  strict  counterpoint,  viz.  "  The 
Art  of  Counterpoint,"  by  the  author  of  Practical  Harmony. 

In  harmonizing  the  following  melodies  the  rules  given  in  Chapter 
IV.  should  be  followed. 

SUGGESTIONS. 

The  chord  on  the  strongly-accented  part  of  a  measure  should 
rarely  be  the  same  as  the  chord  on  the  weak  part  of  the  preced- 
ing measure.  A  chord  on  the  weak  accent  anticipating  the  strong 
accent,  robs  the  latter  of  much  of  the  emphasis  which  should  belong 
to  the  first  count. 

It  is  not  necessary  to  change  the  harmony  with  each  melodic 
note.      The  bass  may  remain  stationary  : 


or  may  pass 
from  fundamental 
to  first  inversion, 
or  vice  versa. 


1 
\ 


u 


In  choosing  between  open  or  close  harmony,  select  that  which 
will  keep  the  voices  in  their  normal  position. 

Open  harmony  is  usually  preferable.      (  See  Chapter  V.  ) 
The  third  of  a  minor  triad  is  often  doubled.      (  See  Ex.  73.  ) 

MELODIES. 


I. 


i 


t§m 


T-^r~^ — 


&t± 


-£?- 


5 


'V 


-<2- 


n 


QpJiJ^JfeN^^^M^i^H 


44 


PR  A  C  TIC  A  L    HA  RMONY. 


fa 


is 


-&- 


&±?=± 


±=fz 


4= 


t 


— 1= 


crtr~- 


I 


5. 


U 


y,^4e)  f^B 


-#-(S2- 


Ip=^ 


r«-fi? 


F^g- 


P 


-5>- 


g^ 


.52- 


I 


8 


BE^ 


sea 


m^g 


=j=ptt= 


■F-i- 


I 


CHAPTER   VII. 

CHORDS. 

THE    SECOND    INVERSION. 

The  second  inversion  is  obtained  by  placing  the  fifth  of  a  chord  in 
the  bass. 

In  this  position  the  notes  above  the  bass  form  the  intervals  of  a 
fourth  and  a  sixth,  and  for  this  reason  the  second  inversion  is  com- 
monly called  the  six-four  chord. 

The  triad  of  C  in  its  three  positions  should  be  figured  as  below : 


Ex.  75. 


Root  position. 

Fi 

rst  inversion. 

Second  inversion. 

/ 

/ 

1-1 

( 

/ 

r? 

o 

72^ 

1 

( 

\                  1-2 

n 

1 

V 

*                 % 

&                   M 

«_ 

8 

5  or  8 

-<s>- 

6 

6 

f 

9 

<?               "II 

f 

!• 

s? 

II 

\ 

->          c 

l| 

II 

When  different  chords  are  to  be  placed  over  an   unchanged  bass 
note,  each  chord  should  have  its  special  figuring. 


Ex.  76 


\ 


3: 


-9r-  «- 


a 


-£v- 

6 


6 
4 


g£| 


^ 


I 

i 


PRACTICAL    HARMOXY. 


45 


In  a  case  like  the  preceding,  each  chord  has  an  equal  part  of  the 
value  of  the  hass  note. 

It  often  occurs  that  the  general  rhythmic  character  of  the  piece 
demands  an  unequal  value  of  the  notes.  Figuring  like  that  in 
example  76  could,  among  other  ways,  be  varied  as  follows : 


Ex.  77. 


Figuring  like  the  preceding  is  vague,  at  the  best,  and  the  choice  ol 
the  length  of  the  notes  must  depend  largely  on  the  taste  of  the  pupil. 

The  second  inversion,  far  from  having  the  sweetness  of  the  first, 
has  a  character  which,  if  not  hard,  is  at  least  very  bright  and 
dominating.  There  is  an  imperious  tonal  force  about  this  posi- 
tion of  the  chord  that  is  so  strong  that  the  root  generally  gives  the 
effect  of  a  tonic.  This  is  especially  true  if  it  is  introduced  on  the 
strongly-accented  part  of  a  measure.  For  this  reason  its  use  is 
subject  to  certain  conditions ;  for,  if  introduced  carelessly  on  any 
note  of  the  scale,  there  would  result  the  effect  of  constant  mod- 
ulation, or  at  least  of  wavering  tonality.  On  account  of  its  power- 
ful tonal  force,  its  use  is  largely  confined  to  the  three  principal  triads. 
When  introduced  on  a  secondary  triad,  especially  if  it  comes  on 
the  accented  part  of  the  measure,  it  gives  the  less  important  triad 
undue  prominence.  From  the  foregoing,  it  will  be  readily  under- 
stood why  this  six-four  chord  is  best  used  on  a  tonic. 

Play  the  following  examples  from  "  Lohengrin  "  and  note  the  dom- 
inating, imperious  effect  produced  by  the  six-four  chord. 


Ex.78 


1 

I 


!'' 


'-- : 


o 


£3 


3      I    s> 


5 


d&£ 


6 

4 


O 


3 


s>   • 


--  m 


m 


<> 


% 


'be* 


1—4- 


>• 


c* 


;-> 


o> 


a 

i 


II 


bo 


*» 


o 


II 


46 


PR  AC  TIC  A  L    HA  KMONY. 


The  six-four  chord,  although  constantly  used  by  modern  musi* 
cians,  is  subject  to  peculiar  conditions.  No  other  chord  demands 
more  delicate  handling,  nor  is  there  one  that  is  more  abused. 

The  laws  governing  its  use  are  among  the  most  important  in 
musical  composition. 

In  every  six-four  chord  in  a  major  key  —  except  that  of  which  the 
root  is  the  leading-tqyie —  there  will  be  found  the  interval  of  a  per- 
fect fourth  between  the  bass  and  one  of  the  upper  notes. 

Whenever  a  six-four  chord  is  introduced  on  any  note  except  a 
tonic,  one  of  the  notes  forming  this  perfect  fourth  must  have  appeared 
in  the  preceding  chord.  When  a  note  has  thus  appeared  in  the  pre- 
ceding chord  it  is  said  to  be  prepared.  If  a  six-four  chord  were  to 
be  written  on  C  it  should  enter  in  one  of  the  following  ways : 

b. 


Ex.  79. 


s- 


-&- 


-&- 


sr 


4 


6 
4 


-&- 


~0~ 


C 


-a. 


II 


In  a  six-four  chord,  on  C,  the-two  notes  forming  the  perfect  fourth 
*tre  C  and  F.  One  of  these  notes  is  prepared  in  each  of  the  above 
example:) ;  at  a  the  F  is  prepared,  at  b  the   C  is  prepared. 

In  the  chord  following  the  six-four  chord,  one  of  the  notes  form- 
ing the  perfect  fourth  should  remain  stationary ;  the  other  should 
descend.     This  is  called  its  resolution. 

b. 


Ex,  SG. 


At  tf,  ir.  the  preceding  example,  the  fourth  is  prepared  in  the 
bass  and  resolved  in  the  soprano;  at  b  the  fourth  is  prepared  and 
resolved  in  the  tenor. 

It  should  be  clearly  understood  that  either  one  of  the  notes  form- 
ing a  perfect  fourth  maybe  prepared,  and  that  this  preparation  need 


PRACTICAL   HARMONY. 


47 


occur  onlv  when  the  fourth  is  formed  between  the  bass  and  an 
upper  voice,  and  may  be  dispensed  with  entirely  when  the  root  of 
the  chord  is  a  tonic. 

In  harmonizing'  a  six-four  chord  it  is  best  to  double  the   fifth  of 
the  chord,  —  that  is,  the  bass  note. 


Ex.  81 


■i 


-SM- 


1 


6 


-&=*: 


1 


The  fundamental,  when  doubled,  produces  a  good  effect  in  pas- 
sages like  the  following,  where  the  fundamental  forms  a  part  of 
the  succeeding  chord. 


Ex.  82. 


If,  however,  the  fundamental  of  the  six-four  chord  does  not  appear 
in  the  chord  folio-wing  the  six-four  chord,  it  is  better  not  to  double 
the  fundamental. 


-!— r— 4- 


Ex.  83. 


As  was  stated  at  the  beginning  of  this  chapter,  any  chord  in  its 
second  inversion,  entering  without  preparation  of  its  fourth,  will 
produce  a  modulation.  From  this  it  will  be  understood  why  the 
second  inversion  on  a  tonic  needs  no  preparation  in  either  major  or 
minor.     A   six-four   chord    on    a    tonic   only   strengthens    its    own 


48 


PR  A  CTICAL   HA  RMON  Y. 


tonality.      This  chord  on  a  tonic   should  always  be  attacked  on  the 
strongly  accented  part  of  the  measure. 


Ex.  84. 


I 


s~ 


?z 


-<9— 


6 
4 


-iS>- 


-<5>- 


-TZT 


=1= 


— «- 


-&- 


1 


-<S»- 


-7Zr 


-&- 


6 

•4 


J2- 


-iS>- 


-£2.- 


I 


I 


When  a  six-four  chord  is  preceded  by  another  position  of  the 
same  chord  it  needs  no  preparation,  as  at  a  ;  when  succeeded  by 
another  position  of  the  same  chord  it  needs  no  resolution,  as  at  b : 


Ex.  85. 


Successive  six-four  chords  are  permissible  only  when  one  is  built 
on  a  diminished  triad  ;  this  fourth  needs  no  preparation.  The  fol- 
lowing would  be  practicable  in  the  minor  mode. 


Ex.  86. 


y 


c 


=£ 


-&- 


s< 


ty 


~s>~ 

6 
4 


--SI- 


o 


III 


(S--  -25*-  -S? 

6 

4 


<S> 

t 


"25" 


-(2- 


"2?" 


II 


Whenever  a  six-four  chord  is  built  on  the  second  degree  of  a 
minor  scale,  as  at  example  86,  the  bass  note  should  not  be  doubled. 

Although  the  second  inversion  is  best  when  used  on  the  principal 
triads,  it  may  occasionally  be  introduced  on  other  degrees  on  the  un- 
acce nted  part  of  the  measure.     Here  it  will  not  have  too  great  tonal 


PR  A  C  TIC  A  L   HA  KMONY. 


49 


importance, 
ing  chord. 


In  such  instances  it  has  more  the  character  of  a   pass- 


On  second  degree. 


On  third  degree. 


Ex.  87. 


± 


w- 


-<s- 

--r 


6 
4 


6 


-@- 


"27^ 


"2^ 


-<5>- 


On  sixth  degree. 
/* N_ 


=2: 


II 


-&- 


6 
4 


6 

t 


9* 


c> 


--&- 


-72~ 


G>- 


& 


f> 


II 


In  each  of  the  six-four  chords  in  example  87,  o?ie  of  the  notes 
forming  the  perfect  fourth  is  both  prepared  and  resolved,  as  explained 
in  examples  79  and  So. 

OBSERVATIONS. 

When  musicians  speak  of  a  dissonance  they  do  not  necessarily 
mean  a  discordant,  inharmonious  combination  of  sounds.  A  dis- 
sonance is  a  chord  that  is  not  accepted  by  the  ear  as  final ;  it  must 
be  followed  by  another  chord.  Dissonances  may  resolve  into  other 
dissonances,  and  indeed,  it  is  a  marked  characteristic  of  the  modern 
school  of  chromatic  harmony  that  they  do  so  resolve;  but,  unless 
thev  eventually  arrive  and  repose  on  a  consonance  there  is  no  satis- 
fying close.  The  following  successions,  although  harmonious  and 
agreeable,  are  dissonances.  No  ear  with  the  slightest  musical 
instinct  could  be  content  with  an  ending  on  any  one  of  them. 


Ex.  88. 


Ex.  89. 


x: 


S§dE8?£s£Bi= 


*£ 


&zx 


1 


i^zte: 


<2_t:J&22_t| 


-3* 


-49-    -s>- 


^i=^=fe=Ei«==^^^^^^ 


JZ- 


-«> 


-&■ 


4*2- 


? 


b* 


m 


YVagnkr. 


fi 


o 


z 


> 


0 

8a 


-  •-. Jr. 


fe     3* 


-P- H- 


8*     &• 


^ 


£      5 


t 


?o 


Bs 


^ 


i 


- 


^p^E^|fe%i 


•     tt* 


r 


-4^ 


r 


> 


5° 


PRACTICAL   HARMONY. 


The  following,    on  the   contrary,  are   consonances,  and  any  one 
heard  alone  would  be  accepted  by  the  ear  as  final. 
a. 


Ex.90. 


JO.- 


-GL- 


-O.- 


-&- 


-&- 


-&- 


-O- 


The  difference,  then,  between  a  dissonance  and  aconsonance  is  this  : 
a  dissonance,  though  oftentimes  more  harmonious  and  satisfying 
than  a  consonance,  must  be  followed  by  another  chord,  while  a 
consonance,  taken  as  an  isolated  chord,  will  be  accepted  by  the 
ear  as  final.  The  best  effects  are  those  in  which  there  is  a  judicious 
use  both  of  consonances  and  dissonances. 


Ex.  91 


\ 
\ 


i£g 


\  kJ- 


Wagner. 


&=P&# 


r-%=^r<i?^^& 


u 


'■>    •  ^ 


w^m 


PRACTICAL    HARMONY. 


5* 


The  chord  following'  a  dissonance  is  called  its  resolution. 

When  dealing  with  dissonances  as  explained  in  Part  II.,  it 
will  be  found  that  the  school  resolution  of  any  dissonance,  demands 
that  the  dissonant  note  shall  progress  down  to  the  next  degree  of 
the  scale. 

The  six-four  chord,  although  not  properly  a  dissonance,  has  this 
characteristic  of  all  dissonances :  it  will  not  be  accepted  by  the 
ear  as  final. 

The  regular  resolution  of  the  dissonant  note,  the  fourth  —  espe- 
cially if  it  be  used  on  a  tonic  where  it  has  the  most  character  — ■ 
follows  that  of  all  dissonances  and  should  descend  to  the  next  degree 
of  the  scale. 


Ex.  92. 


All  that  was  written  in  Chapter  I.  regarding  the  interval  of  the 
fourth  as  having,  at  certain  times,  the  character  of  a  consonance,  at 
other  times  that  of  a  dissonance,  for  which  reason  it  is  called  a 
mixed,  or  neutral  interval,  will  now  be  better  understood :  when 
the  interval  of  the  fourth  comes  between  two  of  the  three  higher 
voices,  as  at  a  in  example  93,  it  is  consonant ;  but  when  it  comes 
between  the  bass  and  any  higher  voice,  as  at  b,  it  is  dissonant. 
.a.  b. 


Ex.  93, 


f 


as: 


^ 


-£•-_ 


6 

t 


-<2- 


[' 

!. 


-7S~^r- 


r> 


-f7* 


-&- 


-<&- 


II 


6 
■I 


6 

1 


n 


A  clear  understanding  of  the  preceding  will  be  of  great  service 
to  the  student  when  he  begins  to  write  strict  counterpoint. 

The  most  frequent  exceptions  to  the  preceding  rules  regarding 
the  six-four  chord,  are  included  under  the  following  irregular 
resolutions. 

I.      Either  one  of  the  two  notes   forming  a   perfect  fourth,  instead 


52 


FRA  C  TIC  A  L   HA  RMONY. 


of  descending,  may  remain  stationary  and  form  a  part  of  the  succeed* 


ing  chord  : 


Ex.  94. 


IT.     A  fourth,  instead  of  descending,  may  ascend  chromatically 


Ex.  95. 


6 
I 


-<&- 


^H 


-- s>- 


-G>- 


~K>- 


-&- 


-#?- 


m 


6 

4 


A  chromatic  change  of  the  fourth,  like  the  above,  always  im- 
plies a  change  of  key.  » 

The  resolution  of  the  fourth  is  often  dispensed  with  by  the  best 
writers,  when  coming  on  a  tonic  in  successions  like  the  following: 


Ex.  96. 


But  all  such  progressions  are  usually  followed  by  harmonies 
which  may  follow  the  six-four  chord ;  and  they  should  be  looked 
upon  as  interrupted  resolutions  of  this  first  chord. 

Many  of  these  "observations"  will  not  find  their  application  till 
later.  It  is  not  expected  that  they  shall  be  fully  understood  at  this 
period,  but  if  they  have  been  carefully  read  the  student  will  be 
well-prepared  for  the  study  of  dissonances  as  they  are  treated  in 
Chapter  XI. 

The  figures  %  followed  by  a  3   or  a  5,  or  either  of  the  chromatic 


PR  A  C  TIC  A  L    HA  RMON  Y. 


53 


signs  t3,  £,  signify  that  two  chords  should  be  written  over  the  same 
bass  note ;  the  bass  note  is  always  the  root  of  the  second  chord. 

S s  <■- 


Ex.  97. 


i 


9i 


«=: 


-(9 — 
& &— 

6  3  or  5 

4 


-N  S~ 


-^j— ttST 


— a^ — ^~ 


g 


3£ 


. 


Ill] 


I    * 


6 
4 


: 


Efc 


IJ 


EXERCISES. 


'•E§S: 


6  6         6  6       6 


— (22- 


6 
4  3 


-<SZ- 


-«-- 


Z5 


==£: 


6 
4  3 


g] 


2.  e§s 


5  6  6 

8  4    6       6  4 

-9 


6 
6    4 


#   # 


J=P 


|2       9 


8 
3 

8 


3  8 

5  3       6  6 

8  5       4  3         4  3 


t9- 


^ 


■<9- 


=«--? 


3-4— ii- 


=t=t 


6 
343 


-| h 


=f= 


.f2. 


-s»- 


I 


6  8  5  6 


=t=: 


E§^ 


6  6 

5    4    3  4  3       8 


-h 


*    0 


SF 


3=t 


4 


t- 


4=3 


-B* 


3 

5 
8 


tj6 

4 


6 
4 


4.  F§aa 


ESEEt 


-<S>- 


-s>- 


-a- 


6 


Q 


__f2- 


•-> 


B4 


-S>— 


P 


O 


-«  — 


a       5 


(2- 


-(9- 


6 
4 


^>  ^ 


IJ 


5    6    6  6  6  6 

8    4,643  )    -  ,         ,-f-  m      646       ,643 


6  6   . 

8    4         8         6  4  J 


6         6 
3  6  4         4 


6.|:3gEgEEm> 


i 


54 


PRACTICAL    HARMONY. 


m$± 


-.|fe 


6 


6 
34 


u 


~tS>- 


-e2- 


s>- 


-G> 


<S>- 


I 


$6 
4 


3  6 


6 - 

it 


6 

4 


6 
4 


-<S>- 


-(9- 


-S>- 


m 


<s>- 


-&- 


6  6  6 

435       643       43 


8 

6-,    5 3,4 
4-*»    3  5  06    3 

1— h  -l— r  — 


1 


CHAPTER   VIII. 

FORM.     THE    PHRASE.     THE    PERIOD.     CADENCE. 

Form,  in  music,  is  the  means  by  which  the  composer  gains  unity 
and  symmetrical  proportions;  it  is  the  frame  in  which  the  musical 
picture  is  placed.  Music  without  rhythmic  order,  melodic  and 
harmonic  relationship  —  without  form  —  would  be  unintelligible 
and  monotonous.  As  form  is  the  outward  expression  of  the  thought, 
there  can  be  as  many  forms  as  there  are  varying:  thoughts.  There 
are  certain  orders  of  musical  form  which  are  more  symmetrica) 
and  gratifying  than  others  :  these  have  been  so  perfected  by  the  great 
masters  that  they  are  almost  universally  accepted  as  the  best  mode 
of  expression. 

The  best  examples  of  form  are  to  be  found  in  what  is  called  "abso- 
lute "  or  "abstract"  music,  in  contradistinction  to  what  is  known 
as  "programme"  music. 

The  smallest  succession  of  notes,  which,  taken  alone,  forms  a  satis- 
fying musical  thought  is  called  a  Phrase.  The  length  of  the  phrase 
varies  according  to  the  length  of  the  thought  to  be  expressed ;  but 
the  most  commonly  used  is  that  of  four  measures. 

Beethoven. 


Ex.  98. 


! 

I  COTS  %  BdL^ztpzezrJi:  t % :p~rS  r~  TSTT  *1 rn 


PRACTICAL   HARMONY. 


55 


It  should  be  noticed  that  in  the  preceding  example  the  rhythm  of 
the  third  and  fourth  measures  differs  from  that  of  the  first  and 
second,  and  that  the  four  measures  are  necessary  to  complete  the  full 
thought.  A  passage  of  four  measures,  in  which  the  third  and  fourth 
are  but  repetitions  of  the  first  and  second,  does  not  form  a  four- 
measure  phrase,  but  is  called  a  Double  Section. 

If  the  third  and  fourth  measures  are  but  rhythmical  repetitions  of 
the   first  and   second    measures,  the  passage  is  still  called  a  Double 


Section. 


Ex.  99. 


=#4=j 


i 


&- 


=1 


m 


Ex.100.: 


tJ 


Beethoven. 

-4 


iF^f^^>=^^=:J^5  5s^ 


ifcz^ 


m 


The  distinguishing  characteristic,  then,  of  a  four-measure  phrase 
is,  that  the  four  measures  are  indispensable  for  the  expression  of  a 
musical  thought. 

The  Period  consists  of  two  phrases  of  equal  length.  As  a  rule 
there  is  enough  similarity  in  the  two  phrases  to  show  that  the  second 
is  responsive  to  the  first,  although  the  second  is  usually  more 
emphatic  and  final. 

Beethoven. 


:x.  101. < 


9^^ 


4-*-^ 


55 


#.-• 


\  ?        0*.      ?  0fi-         A       ^»*  f-     #■     -f- 

v[=:i^-'-^-EE3:-a=:E^|=£Ec-c:E  E=p=EE-E  *  E  E  1=3 


1 
I 


=^S 


0  ■• 


& 


-zl^+ 


UZ» 


p-±.  -•  ^  ••* 


*-  *-#■ 


£      • 


F=F 


-x 


FiF=r-=T=t=pl 


m 


When  one   speaks  of  a   period  one   means  the    period    of   eight 
measures,  similar  in  construction  to  the  preceding.   There  should  be 


*6 


PRACTICAL   HARMONY. 


enough  melodic  and  harmonic  order  in  the  period  to  form  by  itse  I 
a  complete  musical  sentence.  There  are  other  periods  of  different 
lengths  but  they  are  nearly  always  qualified,  as,  for  example,  "six- 
measure  period,  "  "  seven-measure  period,  "  "  ten-measure  period." 
Without  such  qualification  the  period  of  eight  measures  is  under- 
stood. 

CADENCES. 

A  cadence  is  the  close,  more  or  less  definite,  of  a  musical  thought. 
It  is  to  music  what  punctuation  is  to  prosody ;  it  divides  the  thought 
and  gives  the  proper  emphasis. 

The  Authentic  Cadence  is  the  strongest.  It  is  formed  by  the 
chord  of  the  dominant  followed  by  the  tonic ;  the  latter  chord  must 
always  fall  on  the  accented  part  of  the  measure. 

The  following-  are  forms  of  the  authentic  cadence : 


Ex.   102. 


\ 


3i  |3?fe|33i^|^#=f| 


"Z7 


^ 


^ 


J2- 


•*-  _£Z^€l 


-£&*- 


6 
6    4 


_(S2_- 


-O- 


-&■&■ 


-O.. 


-72~ 


I 


Illustrations  I  and  II,  with  the  root  of  each  chord  in  the  bass  and 
with  the  soprano  ending  on  the  tonic,  -are  termed  the  Perfect 
Authentic  Cadence.  The  same  harmony,  but  with  either  the 
soprano  ending  on  a  note  other  than  the  tonic,  or  either  or  both 
chords  inverted,  are  termed  the  Imperfect  Authentic  Cadence. 
See  III,  IV,  V,  VI,  and  VII  in  preceding  example. 

The  Plagal  Cadence,  consisting  of  the  subdominant  followed  by 
the  tonic  is  particularly  agreeable  when  following  the  Authentic. 


Ex.    103 


Authentic  Cadence.    Plagal  Cadence. 

jy 

II 

<y 

S3 

&            \\ 

x& — ^ 1 

r. 

g 

V            \\ 

^jZ — ^ 1 S> ' e* ' — S> "J 

6 
4 

cv     ^ 

II 

*  I- 

II 

s 

a. 

*3 

&■         II 

1  1 

The  Plagal  Cadence  may  be  used  without  being  preceded  by  the 
Authentic 


PRACTICAL    HARMONY. 


5? 


The  Half  Cadence,  as  its  name  suggests,  marks  a  short  rest; 
it  usually  comes  between  the  members  of  a  phrase  or  period.  T1^ 
half  cadence  is  usually  made  on  the  dominant,  preceded  bv  any 
other  chord. 


Ex.    104. 


-9—4 I— J- 


-<St- 

-<s>- 


I 


-4- 

"25!- 


— I- 


-m- 


-25!~ 


II 


-S>- 


p3EEEf 


6 

I 


]| 


The  Deceptive  Cadence  —  sometimes  called  the  false,  inter 
r  up  ted,  or  broken  cadence  —  consists  of  the  dominant  followed  b] 
any  degree  of  the  scale  except  the  tonic.  It  is  often  followed  b» 
another  degree  of  the  same  scale,  sometimes  by  a  change  of  key. 


Ex.   105 


i 

II 


& 


~N   /-~ 


I  -&^-  -&—  |<S>—  F— <9-\<S>-  ~-SL— H 


<? 


-£?— i-w— 


6 

-fS>- 


"25^ 


3^: 


_z?- 


rte- 


The  character  of  a  cadence  depends  largely  upon  what  has  precedei 
it.  The  authentic  cadence  is  most  frequently  preceded  by  a  si* 
four  chord  on  the  tonic.  This  use  of  the  six-four  chord  is  the  mosl 
common  and  the  best. 


Ex.   106 


I 


-s    S N   S" 

-4-4,-  l.fg-p,^. 4 

s!tI-        -Vs-  &- 


-4 

-«4-5) 

2        <>  St+- &-;\J>G>1-W~\<>-0 


L| 1 L£?-'-#-L ' L-!£ilT, 


A^-r- r4- 


ii 


EXERCISES. 

1.  Compose   a   short   bass   in  C,  ending    with    Perfect   AuthentM 
Cadence. 

2.  Compose  a  short  bass  in  i/',  ending  with  Imperfect  Authentic 

Cadence. 


5S 


PRACTICAL   HARMONY. 


3.  Compose  a  short  bass  in  A,  ending  with  Plagal  Cadence. 

4.  Compose  a  bass,  longer  than  the  preceding,  in  A  b,  dividing  it 
with  the  Half  Cadence,  and  closing  it  with  the  Perfect  Authentic 
followed  by  the  Plagal.  ■ 

^.   Compose  a  bass  in  d  according  to  the  formula  in  No.  4. 

Before  harmonizing  the  succeeding  melodies,  the  student  should 
read  again  all  that  was  written  in  Chapter  II.  regarding  melodic  and 
harmonic  progressions,  as  well  as  the  "  suggestions"  at  the  close  of 
Chapter  IV. 

The  chapter  on  the  second  inversion  should  also  be  re-read. 
This  done  the  student  should  divide  the  following  melodies  into 
phrases,  seeking  that  cadence  for  the  close  of  a  phrase  which  his 
musical  instinct  tells  him  is  best  adapted  to  its  character.  After 
the  cadences  have  been  decided,  the  other  harmonies  of  the  phrase 
will  more  naturally  suggest  themselves. 

The  second  inversion  is  a  most  important  factor  in  the  cadences; 
it  makes  them  emphatic  and  final.  (See  Ex.  106.)  Although  it  is 
not  absolutely  indispensable,  it  should  be  employed  whenever  the 
nature  of  the  phrase  permits  it.  As  its  use  is  somewhat  diffi- 
cult, it  should  be  seldom  introduced  except  in  cadences,  and  then 
under  the  conditions  recommended  in  this  and  the  preceding  chapters. 

Whenever  the  nature  of  the  melody  permits,  change  the  harmony 
with  each  note.  Sometimes  it  will  be  best  to  retain  one  harmony 
during  two,  or  perhaps  three  notes.  In  this  the  pupil  must  follow  his 
musical  instinct. 


EXERCISES. 


=1 


itait 


I 


-EE£=t 


^ 


■*—&■ 


fe=f 


P= 


■&  —  &T 


■&- 


=£ 


-m-ji- 


<S>—T^- 


o 


2. 


1 


-*>- 


-G>- 


-Q.- 


-&- 


lt5'- 


-<S>- 


I 


PRACTICAL    HARMONY. 


59 


~&- 


T- 


■&- 


&---& 


^P© 


II 


6. 


-f2 — <S>-  -g) — &- 


■&—&- 


-&- 


-&- 


-&- 


&—& 


<s 


Andante. 


+*9 


U-fc-U-Ptf-—  ml  1   fr  I  I     "tlfWmfT 


M  > 


^stitS^i 


T=t 


II 


CHAPTER   IX. 

MODULATION.     TONAL    RELATION.     MODULATIONS    OF   THE    FIRST 
ORDER.     EXERCISES.     MODULATIONS    OF   THE    SECOND 
ORDER.     MODULATIONS    TO    REMOTE    KEYS. 
PASSING    MODULATIONS.     HAR- 
MONIC   SEQUENCE. 

Modulation  is  the  art  of  moving  from  one  key  to  another.  If  a 
composition  of  more  than  a  few  phrases  in  length  were  to  remain  in 
one  key  the  monotony  would  be  wearisome.  Digressions  from  the 
original  key  are  made,  to  gain  variety.  The  possibilities  in  modula- 
tion are  probably  limitless.  From  Mozart  to  Brahms  there  has  been 
a  constantly  widening  latitude.  Art  is  progressive ;  that  which 
to-day  seems  impossible,  may  to-morrow  be  accepted.  Hence,  it 
is  wiser  to  say  what  one  may  do,  rather  than  what  one  may  not  do. 
The  mo6t  helpful  theory  is  that  which  enables  one  to  analyze,  under- 
stand, and  better  appreciate  the  compositions  of  acknowledged 
masters.  The  question  ought  not  to  be  "  Is  tins  passage  in  Bach, 
Beethoven,  Schumann,  or  Wagner,  wrong?"  but  rather,  "Should 
not  the  old  system,  which  cannot  account  tor  the  new  effect,  be  modi- 
fied.' "  Practice  should  precede  theory,  and  one  function  of  a  new 
text-book  is  to  adapt  the  old  rule  so  that  it  shall  include  the  latest 
discovery  of  a  great  composer. 

It  should  be  understood  clearly  that  modulation  is  the  method 
we  employ  to  get  to  a  new  key;  it  is  the  process  and  nol  the  result  ; 
it  is  the  means  by  which  the  change  is  effected  and  nol  the  key  into 
which    we    pass.      A    sudden    change    of   key    dot's    not    necessarily 


So 


PRACTICAL   HARMONY. 


include  a  modulation.      If  the  chords  of  C  and  Gb  were  heard  suc- 
cessively : 


Ex.   107 


I 


jffi- 


i 


1&- 


& 


1 


there  would  be  no  modulation,  only  a  brusque,  unsatisfactory  leap 
from  one  key  to  another.  If  the  two  keys  were  united  by  a 
succession  of  chords  having  one  or  more  notes  in  common,  the 
progression  could  legitimately#be  called  a  modulation: 


Ex.   10S. 


-ul?-z?- 


g>— ftg*- 


£2_ 


frgl      k 


=fc 


£ 


» 


ill 


I 


It  will  be  seen,  later,  that  it  is  not  always  necessary  to  have  a  note 
common  to  successive  chords. 

One  should  realize  that  the  same  rules  apply  to  harmonies  in 
different  keys,  as  to  harmonies  remaining  in  one  key,  and  that  sat- 
isfying modulations  are  governed  by  intelligible  melodic  movement 
of  the  different  voices. 

With  a  clear  appreciation  of  the  principles  of  tonal  relation,  it 
will  nearly  always  be  possible  to  understand  the  effects  of  agreeable 
modulations,  even  of  those  which  seem  intricate  and  remote. 

Whatever  means  one  may  employ  to  effect  a  modulation,  there 
is  really  but  one  principle  to  be  kept  in  mind:  destroy  the  tonality 
of  the  old  key,  and  prepare  the  ear  to  receive  the  new.  Whether  the 
modulation  shall  be  brusque  and  startling,  or  well-prepared  and 
gradual,  depends  wholly  upon  the  effect  desired. 


TONAL    RELATION. 

CLOSELY    RELATED    KEYS. 

Keys   are    said    to    be  related  when  they    look  and  sound   alike. 


PA  A  C  TIC  A  L    II A  RMONY. 


6l 


The  keys  most  nearly  related  are  those  whose  signatures  are  the 
same,  and  those  whose  signatures  contain  one  sharp  or  one  flat 
more,  or  less. 

The  nearest  related  keys  to  C  arc  its  minor,  a  ;  its  dominant,  G; 
and  the  relative  minor  of  G,  r;  its  subdominant,  F;  and  the  relative 
minor  of  F,  d.  They  may  be  represented  by  the  next  five 
ascending  notes  of  the  scale  : 


Ex.    109. 


Nearest  related  keys  to  C. 
d.        e.        F.        G.        a. 


-&- 


This  is  relatively  true  of  all  major  scales. 

Minor  keys  have  equally  five  related  keys  which  are  represented 
by  reversing  the  order  and  descending  five  notes  of  the  scale  : 


Ex.  1  10. 


Nearest  related  keys  to  a. 
G.        F.         e.        J.        C. 


II 


The  nearest  kevs,  then,  to  any  major,  are  its  dominant,  its  sub- 
dominant,  and  the  relative  minors  of  these  three  keys. 

The  nearest  related  kevs  to  any  minor  are  its  dominant  and  sub- 
dominant  minors,  and  the  relative  majors  of  these  three  keys. 

The  tonal  relation  existing:  between  more  remote  kevs  will  be 
explained  later. 

MODULATION. 
Continued. 

A  modulation  is  effected  by  introducing  notes  characteristic  of  the 
key  to  which  wc  are  going,  but  foreign  to  the  key  we  are  leaving. 
Two  chords  at  least  are  indispensable  to  determine  a  key. 

The  phrase  at  a  in  the  succeeding  example,  is  presumably  in 
C;   by  the  introduction  of  g#,  as  at  /;,  the  key  is  probably  in  a: 


Ex.  1  1  1 


62 


PR  A  C  TIC  A  L    HA  RAW  NY. 


If,  in  successive  chords,  a  note  common  to  each  chord  is  to  be 
raised  or  lowered,  the  alteration  should  be  effected  chromatically, 
i.e.,  the  change  should  be  made   melodicallv  or  in  the   same  voice. 


Ex.  112 


-AL iS2_ 

—a— 

\      I 

H&— 



— ^ — 

II 

XT — & 

1 — <s> — 

jSL. 

-H 

5' 

— a 

— a 

II 

S 

1 

When  a  note  first  appears  in  one  voice,  followed  by  another  voice 
taking  this  note  chromatically  altered,  there  results  a  harsh  effect 
known  as  "false-relation,"  or  "cross-relation." 


Ex.   1  13. 


The  disagreeable  effect  of  a  "false-relation"  may  be  realized  by 
playing  the  following  in  quick  succession  : 


Ex.    1  14, 


9- 


F 


:p=-= 


m 


There  are  certain  "  false-relations  "occurring  between  the  bass  and 
an  intermediate  part  which  are  not  disagreeable.  Experience  can 
best  determine  the  limit  of  such  progressions.  Among  those  most 
frequently  found  in  the  writings  of  acknowledged   masters  are  the 

following  : 


Ex.   1  1  5. 


yiEi&j 


3=  EgE  p=  bg^i 


1^0 


PR  A  C  TIC  A  L   HA  RMONY. 


63 


The  preceding  example  at  b  can  hardly  be  called  a  "false-rela- 
tion," because,  although  this  relation  exists  between  the  bass  and 
alto,  the  alteration  really  occurs  in  the  same  voice,  i.e.,  the  alto. 

The  skip  of  the  diminished  fourth  at  a,  example  115,  calls  for  the 
explanation,  that,  in  modulations,  more  liberty  is  allowed  in  the 
progression  of  the  parts.  This  is  especially  true  of  the  bass.  In 
modulations,  when  the  bass  moves  to  the  leading-tone  of  the  new- 
key,  many  intervals  which  would  otherwise  be  difficult,  are  easy  of 
intonation  and  therefore  permissible  : 


Ex.   1  16. 


I 


Dim.  fifth.         Dim.  fourth.     Aug.  fourth. 


Aug.  second. 


As  a  rule  it  is  better  not  to  double  a  note  which  is  to  be  chro- 
matically altered  : 


Ex.  1  17. 


I 


y 

S3 

/T        " 

fv\     « 

v  7      % 

l) '      &                    ■" 

c^* 

II 

y. 

X                   1 

J             <3 

JK5              1 

w-                 II 

nor,  as  a  rule,  will  the  interposition  of  one  intermediate  chord  destroy 
the  effect  of  a  "  false-relation  :  " 


Ex.   1  18. 


This  relation,   however,   coming  between  the  last  chord  of  one 


6i 


PRACTICAL   HARMONY. 


phrase  and  thejirst  chord  of  a  succeeding  phrase,  is  permissible. 
The  following  examples  are  taken  from  Bach  : 


Ex.   119 


W 


-(St- 


^=g 


w- 


7?~yx~&~ 


£i 


(2 (2 , fZ , O.- 

9%jg jg- 


-<S>- 


1 


sa± 


i$2l=^: 


-<St tH- 


-f2 (=2_ 


-I ts>- 


r 


y. 

~s» — I 


The   note  to  be   chromatically   altered    may   be   doubled   in  pro- 
gressions like  the  following,  where  there  is  strong  contrary  motion. 


Ex.  120. 


I 


-&L 


W- 


--m- 


-(&- 


i 


-&- 


-(2- 


I 


The  note  chromatically  altered  should  rarely  be  doubled,  unless 
moved  to  by  contrary  motion : 


:x.  i2i./ 

( 


Bad 


Good. 


5WJ.3 


\^<2- 


H?2-     ■*- 


—& — — Z?_ 


-0- 


II 


-iS1- 


l§3 


PRACTICAL    HARMONY. 


65 


The  regular  or  most  natural   resolution  of  a  note  chromatically 
raised,  is  to  the  note  a  semitone  above : 


Ex 


.  122.<J 

I 


iT-g" 


=^: 


I — <s>- 


~B~ 


-O.- 


-Q.- 


II 


The  regular  or  most  natural  resolution  of  a   note  chromatically 
lowered  is  to  the  note  a  semitone  below: 


Ex.  123 


\ 


-P- 


9 


T-^- 


-I <5> 


II 


In  place  of  this  so-called  "regular  resolution"  the  altered  note 
may  remain  stationary,  or  it  may  change  enharmonically  : 


Ex.  124. 


/-" 


Remaining  stationary. 


Changing 
enharmonicallv. 


92=^F^=±?gI=t^==g=t^ 


=^=F 


-e>- 


-Q-- 


^=fe: 


te^pM^g^g 


r> 


:F- 


F 


THE    DIFFERENT    ORDERS    OF    MODULATION. 

Modulations  are  divided  into  two  Classes  or  Orders. 

Modulations  of  the  first  order  are  those  that  differ  only  in  oi>e 
accidental,  either  in  signature  or  scale  construction.  A  modulation 
from  C  to  G  would  be  of  the  first  order,  because  there  is  but  one 
differing  note  in  the  construction  of  the  two  scales  — F#.  From  C 
to  e  would  not  be  a  modulation  of  the  first  order,  because,  although 
there  is  but  one  accidental  more  in  the  signature  of  <"  than  C  (  \'%  ) 
the  construction  of  the  minor   scale   calls  tor   the   seventh    note    (</) 


66 


PRACTICAL   HARMONY. 


to  be  chromatically  raised,  which  makes  two  accidentals  more  in  e 
than  in  C. 

Modulations  containing  more  than  one  accidental  are  of  the 
second  order. 

The  key  of  C  has  five  closely-related  keys,  three  of  which  (  a, 
G,  and  F  )  are  of  the  first  order,  and  two  (  e  and  d  )  are  of  the 
second  order.      This  is  relatively  true  of  all  major  keys. 


MODULATIONS    OF    THE    FIRST   ORDER. 

To  modulate  from   C  to   G,  the  modulation  can  be  effected  by 

introducing  any  chord  —  except  the  chord   on  the   leading-tone  — 

which  contains  F  J,  the  characteristic  note  of  the  key  of  G,   and 

following  this  by  another  chord  or  other  chords,  defining  the  new 

key.      There  would  be  but  two  chords  containing  F#:  those  formed 

on  the  third  degree,  and  the  fifth  degree : 

x  x 


Ex.  125 


^ti: 


41 


J- 


i 


•- 


r 


A 


? 


0 


All  that  was  written  in  Chapter  IV.  concerning  the  weak  tonal 
effect  of  the  triad  on  the  third  degree  of  the  scale,  and  in  conse- 
quence its  restricted  use,  is  especially  true  in  modulations.  It  is 
the  weakest  degree  upon  which  to  enter  the  new  key. 

It  will  be  remembered  that  the  succession  from  the  fourth  to  the 
third  degree,  with  the  following  disposition,  is,  on  account  of  the 
tritone,  very  disagreeable. 


Ex.  126. 


~N 


t§- 


^ 


I 


-&- 


-<S2- 


-&- 


-<2- 


I! 


In  modulations,   the  progression  from  the  fourth  degree  of  the 
old  scale  to  the  third  degree  of  the  new  is  nearly  as  objectionable  : 


Ex.  127. 


s 

I 


-<9- 


-O. 


— <5>- 


I 


PRACTICAL   HARMONY. 


6* 


Note.  The  student  is  sooner  or  later  puzzled  to  explain  why  it 
is  that  the  successions  from  the  fifth  degree  to  the  fourth  degree, 
and  the  fourth  degree  to  the  third  degree,  are  disagreeable : 


Ex.    12S 


M~ 

(k~%~ 

%- 

<? 

%J        & 

-O.- 


_<2_ 


-&- 


\-<s>- 


5th       4th     4th 


— &- 

-&- 

-S>- 


-O.- 


II 


3d 


while  the  same  successions  reversed,  i.e.,   from  the  fourth  degree 
to  the  fifth  degree,  and  from  the  third  degree  to  the  fourth  degree, 


are  agreeable 


Ex.  129 


1 


T— <S>- 


-&>- 


-&- 


4th        5th         3d       4th 


In  art  there  are  many  things  which  cannot  be  explained.  Any 
attempt  to  explain  the  tritone  is  useless  and  illogical ;  it  is  suffi- 
cient  to   realize    that  one    progression   sounds  good,    another,  bad. 

To  modulate  from  C  to  F,  the  modulation  can  be  effected  by 
introducing  any  chord  —  except  the  chord  on  the  leading-tone  — 
which  contains  bv,  the  characteristic  note  of  the  key  of  F,  and 
following  this  by  another  chord  or  other  chords  defining  the  key. 

Note.  In  the  following  exercises  the  modulations  are  to  be 
made  in  the  fewest  possible  number  of  chords.  The  modulating 
chords  are  to  be  considered  as  parts  of  a  phrase. 


GENERAL    RULE. 

The  old  key  may  be  quitted  from  a  chord  formed  on  any  degree 
of  the  scale  —  except  the  seventh  —  and  the  new  key  entered  on  any 
degree  of  the  scale  —  except  the  seventh  —  containing  the  charac- 
teristic note.  To  the  rules  for  melodic  progression  given  in  Chap- 
ter II.  should  be  added  the  progressions  in  example   I  16. 


68 


PRACTICAL  HARMONY. 


EXERCISES. 

I.  T<\  modulate  from  any  major  key  to  its  dominant.  Leave 
the  key  of  C  from  a  chord  formed  on  the  first  degree  in  root  posi- 
tion and  inversions,  entering  the  key  of  G  on  its  dominant. 

The  following  example  shows  the  general  order  to  be  observed  : 


Ex.  130 


-<5> 


From  root  position.  From  first  inversion.  From  second  inversion 


^ 


-&- 


jGL- 


-s>- 


~w- 


-a.. 


s 


5E 

F       1  - 

t=f_ 

a 

— <s>— 

~~  H 

XT — &~ 

1 — ^ 

L'^— 

— i& — 
-<s>- 

hg — 

— & — i 

TO " 

Bt- 

GS 

~&S>— 

H 

^r         f? 

1 1 

1 

II 

Leaving  C  from  root  position,  entering  G  on  inversions  of  the  dominant. 


II.  Leave  the  key  of  C  from  chords  built  on  each  degree  of  the 
scale  —  except  the  seventh  —  i.e.,  the  second,  third,  fourth,  fifth,  and 
sixth  degrees,  entering  the  key  of  G  on  its  dominant.  Inversions  of 
chords  may  be  used,  and  as  many  examples  as  possible  of  each 
progression  should  be  made.  The  rules  given  for  the  six-four  chord 
in  Chapter  VII.  should  be  observed. 

III.  To  modulate  from  any  major  key  to  its  subdominant. 
Leave  the  key  of  C  from  each  degree  of  the  scale- — -except  the  sev- 
enth —  entering  the  key  of  F  on  the  fourth  degree.  The  new  key  is 
entered  on  the  fourth  degree,  because,  in  modulating  to  the  key 
a  perfect  fourth  above  the  characteristic  note  of  the  new  scale 
occurs  on  the  fourth  degree. 

The  modulation  from  the  third  degree  of  C  to  the  sub-dominant 
of  F  will  be  found  very  difficult  on  account  of  the  tritone.  One 
should  remember  that  all  faulty  progressions  are  softened  by  the 
ust-  of  the  first  inversion. 

IV.  To  modulate  from  any  major  key  to  its  relative  minor.  In 
this  modulation  the  new  key  cannot  be  clearly  defined  except  by 
the  use  of  its  dominant. 


PR  A  C  TIC  A  L   HA  RMONY. 


69 


JVbte.  The  diminished  triad  on  the  second  degree  of  the  minor 
scale,  although  not  containing  the  characteristic  note  —  leading- 
tone  —  of  the  scale,  is  most  useful  in  determining  a  modulation.  In 
the  following  examples,  the  diminished  triad  should  be  considered 
as  on  the  second  degree  of  the  scale  of  a,  and  not  as  on  the  seventh 
degree  of  the  scale  of  C. 


Ex.  131. 


This   will   be  more  fully    explained  in  "  Harmonic   Sequence.  " 

Leave  the  key  of  C  from  chords  built  on  each  degree  of  the 
scale  — except  the  seventh —  entering  a  on  the  dominant. 

V.  To  modulate  from  any  minor  key  to  its  relative  major. 
Leave  a  and  return  to  C  on  the  fifth,  the  third,  and  the  first  degrees. 
The  entrance  to  the  new  key  on  the  dominant  will  be  found  the 
most  decisive. 

For  convenience,  the  relatives  are  condensed  here  :  Each  major 
kev  has  five  closely  related  kevs,  three  of  which  are  of  the 
first  order  and  two  of  the  second  order.  For  example,  C  has  for 
relatives  of  the  first  order  a  minor,  G  major,  and  F  major,  and 
for  relatives  of  the  second  order  d  minor  and  e  minor. 

Each  minor  key  has  five  closely  related  keys,  only  one  of  which 
is  of  the  first  order.  A  minor  has  for  relative  of  first  order,  C  major, 
and  for  relatives  of  second  order  G  major,  F  major,  e  minor,  and  d 
minor. 

If  the  teacher  think  best,  he  should  now  arrange  modulations 
of  the  second  order. 


OBSERVATIONS. 

CONCERNING    MODULATIONS    TO    REMOTE    KEYS. 

It  is  of  great  importance  that  the  chord  or  chords  forming  a  remote 
modulation  be  of  sufficient  duration  to  prepare  the  new  key  ;  and 
as  a  rule,  it  is  best  for  the  more  important  chords  to  be  placed  on 
the  strongl)  -accented  part  of  a  measure. 

A  succession  of  chords  containing  material  for  an  effective  modu- 
lation  may  be   made  thoroughly  ineffective,  either  by  introducing 


7o 


PR  A  C  TIC  A  L   HA  RMON  Y. 


the  chords  on  the  weak  part  of  the  measure,  or  by  giving  them  so 
little  time  and  emphasis  that  the  modulation  is  indecisive. 

In  general,  a   modulation  is  as  much   more   satisfactory  as  there 
are  notes  common  to  the  modulating  chords. 

Among  other  ways,  satisfactory  modulations  to  remote  keys  may 
be  effected  by  the  following  means  : 

I.      Major  chords   may   succeed    each  other   with    good    effect, 
provided  they  have  one  note  in  common  : 

S N    S 


~> 


■N  S~ 


:x.  \32.l 


:fe 


"S>- 


-(52- 


— \ter~ — r 


II 


II.  By  the  use  of  chords  which  alone  do  not  produce  a  definite 
modulation  but  are  common  to  several  keys.  In  the  following 
succession  : 


.   133. ^ 


-<s>- 


-&- 


9i- 


— & 


^5?^ 


[I 


The  second  chord  may  be  considered  as  if  in  the  key  of  F,  and 


thus  leading  to  that  kev  : 


Ex.  134 


! 


-v 


%- 


C/  -     ' 


-<52_ 


g  -«- 


-G>- 


-(52- 


6 
4 
-&- 


9^F 


-&- 


& 


C 


-f5>- 


-G>- 


I 
1 


or  as  if  in  the  key  of  a,  and  leading  to  that  kev  : 


Ex.  135 


-&- 


sr 
~>2~ 


sr 


-&-  -&- 


<s 


-S>- 


-72- 


t& 


G> — 


J2Z 


.a. 


-a. 


-<5>- 


sr 


i 


PRACTICAL   HARMONY. 


7* 


or  as  if  in  the  key  of  B  9  or  69,  and  leading  to  either  one  of  these 
keys : 


Ex.  136, 


B?  or  lb 


-fe= 


II 


-<2-  2iZ- 


— ^- 


3^ 


-9«s>- 


II 


III.  By  enharmonic  change 


Ex.  137 


-&S>- 


:^ 


55= 


3«: 


-<52- 


IV.   By    several    modulations    into   closely  related  keys,    leading 
gradually  to  a  remote  key  : 


Ex.  13S 


1 


=ff^=^=F=d-^F^- 


~^M 


.1 (_ 


~^- 


II 


Note.  The  early  masters  rarely  used  modulations  to  keys  other 
than  the  five  which  are  called  the  nearest  related.  .  If  keys  were 
used  not  closely  related  to  each  other  —  as  F  and  G  —  it  was  only  in 
cases  where  these  two  would  be  closely  related  to  the  principal 
key  of  the  piece.  For  example,  F  and  G  would  be  closely  related 
to  C. 

One  must  not  suppose  that  the  preceding  examples  exhaust  the 
les  uirces  of  modulation.  The  possibilities  are  too  numerous  to 
catalogue. 

PASSING    MODULATIONS. 

It  was  stated  at  the  beginning  of  this  chapter,  that  a  modulation 
cannot  be  determined  by  one  chord,  even  though  this  chord  contain 
a  note  or  notes  foreign  to  the  principal  key.  A  phrase  may  contain 
chords  having  notes  foreign  to  the  key  and  yet  not  destroy  the 
unity  of  the  principal   key.     Such  are  termed   "passing  modula- 


72 


PRACTICAL   HARMONY. 


tions,"  "transitive  modulations,"  or  "borrowed  chords."     Anew 
key  is,  in  general,  rarely  determined  except  by  the  aid  of  a  cadence. 


In  the  following : 


Ex.  139, 


i 


& 


-& 


5% 


-s>- 


-J- 

-<st- 


1 


7^ — <9- 


s>- 


<5>- 


-I     ,    1—4- 


2? fiT- 


^ 


-p-^,:^-^ 


_0Z__ 


-i5>- 


— f2- 


.^-i^- 


- 


gr 


■iS>— 


ST-" 


i 


o 


-«-hg 


=4=4: 


-iS- 


:J^=t 


-<9- 


S 


o 


"s?_ 


-5<- 


L>5h 


-sf- 


-<s- 


II 


-&-  -<s-   -&-  -gh 


€-- 


-s>- 


-9-       -S>- 


^i=zp= 


EEE$d 


e 


E 


5E 


pr^ 


r 


^=5 


"S^ 


-19- 


-7? 


I] 


Although  here  are  notes  foreign  to  the  key  of  C,  there  is  no  mod- 
ulation. It  is  best  to  look  upon  those  chords  containing  the  foreign 
notes  as  borrowed  from  other  keys. 

Note.  When  the  prevailing  mode  of  a  piece  is  major,  chords  are 
often  borrowed  from  minor  keys.  When  the  prevailing  mode  is 
minor,  chords  are  rarely  borrowed  from  major  keys,  because  the 
major  chords  imply  too  strongly,  a  modulation. 

From  this  point  the  student  should  unite  in  one  note  all  those 
notes  which  may  be  repeated  in  a  measure.  The  few  exceptions 
should  be  explained  by  the  teacher,  as  they  occur. 


Ex.    140. 


~s>- 


?— -0- 


T^ 


instead    of 


I 


-4—4—4—4- 


:*=*=3|=*:=H 


& 


Jl 


EXERCISES. 

MODULATIONS    OF    FIRST    ORDER,    AND    BORROWED    CHORDS. 

Allegretto. 


!.[« 


-P= 


t 
I   * 


*=£ 


*     6 


6  # 


PRACTICAL  HARMONY. 

I       6       6       6         % 3JJ    | 


73 


6  a 
6  4  J 


^ 


iz=t 


• — &- 


^EElflS? 


-g» &~ 


^-<s>- 


m 


-m — »- 


t 


E 


V 


6 

4         6 


gES^&^E^Egjggg 


e 

4 


5     3  6  3  8  3 

3    5  4  5  3  5 


8  -  § 

,4  8  3 

P6  -  5 


^fcs 


W 


C' 


■Ts 


■5- 


~^y 


Adagio.  s 


«        6        4 


6J 

a     4* 


2. 


z^tfi 


=^4:=^: 


-^ 


^ 


-*2-# 


EzEEi^S 


6  6       j, 

6    6.     4  4       $ 

r4d: 


-z*- 


25 


^5 


q    

586  6  6        6, 

3    5    4     6    .43    34345, 


(Hi 


"??- 


^5T^- 


6 
6   .   4 


fr- 


it 


^•^fjgZg-(g 


{EE^EEEEEt 


* 


s^i 


<s^ 


■5 


1 


Cantabile. 


s^^s^^^a 


E*3t 


±F- 


-.6' — ^-«- 


&--•-* 


lt=l 


^ 


F 


c. 


:i=2-frs>- 


£=£ 


F.  Vd.SeeEx.131.jK    


Allegretto. 


4.  §i|=^  a 


95 


t): 


rr—  <^- 


(S 


SECOND   ORDER. 

6 
6  4 

?2= 


=F 


6 


£ 


^ 


9*  1  si 


^^iii 


6       5$ 

_(g  •     - 


-|SLi_ 


F— («- 


6  5  J 

-<a-* 


1 


6 
6  4 


!» 


si  ^m^^mm^ 


7* 


PRACTICAL    HARMONY. 


6 

4  3 


6  4      3 


3* 


^-•^ff^ 


ffi 


«*-=- 


3  /-n 


-($•- 


:p: 


iS>- 


-(S2. 


L<S-i- 


II 


Andante. 


5. 


9* 


b==2 


-<&■- 


REMOTE    MODULATIONS. 

t-5b  b      6b5b      6 


-(5>- 


«*— 


-^^ 


sb 


m 


zte^^Ez^fea^L^zz 


^i±= 


6  .     u6     .    4       3 


22 


-<&- 


^  • 


■^— g>- 


sj     6       5*  5*     sjf    sb  be 
S       J       **  S*     t    ± b 


© 


9** 


be  sb       sb 
b4  s       ,b 


5$ 

3$ 


5> 


5$ 
3       It 


-(«- 


S* 


se 


-22- 


_(2- 


Si 


3ZZ£ 


-(5»- 


-»- 


s>~ 


-G>- 


— <&- 


-<S>- 


6 
I 


-Ol- 


^r 


-&- 


j2- 


1 


HARMONIC    SEQUENCE. 

In  sequences,  the  ear  being  gratified  by  a  regularly  recurring 
responsive  figure,  certain  harmonic  or  melodic  successions  may  be 
introduced  which  would  otherwise  be  disagreeable. 

The  most  pronounced  of  these  are  the  use  of  the  triad  built  on  the 
leading-tone,  which  we  have  not  used  before,  and  the  freer  use  of 
the  six-four  chord. 

The  triad  built  on  the  leading-tone  when  heard  alone  : 


Ex.  141 


is  weak  and  disagreeable,  but  when  heard  in  sequence  : 

x 


Ex.  142. 


it  becomes  more  agreeable. 


PRACTICAL   HARMONY. 


/5 


The  six-four  chord  may  be  used  on  any  degree  of  the  scale ; 
provided  the  fourth  is  prepared  and  resolved  according  to  the  rule 
in  Chapter  VII.  : 


Ex.  143. 


*=£± 


The  chord  of  the  sixth  is  much  used  in  sequence 

4- 


Ex.   144. 


^ 

-£?- 


JG>- 


&- 


T=f 


■»-hs: 


■&- 


&- 


— i- 


I 


I 


w 


The  melodic  intervals  prohibited  in  Chapter  II.  under  "Melodic 
Progression"  are  permissible  in  sequence.  It  is  best  not  to  use 
these  intervals  in  the  first  measures,  which  form  the  model,  as 
they  would  there  be  difficult  of  intonation.  After  the  figure  has 
been  announced,  any  of  these  intervals  may  be  used. 

The  model  should  contain  as  many  of  the  principal  triads  as  possi- 
ble, and  must  conclude  with  one  of  them. 

The  perfect  symmetry  of  the  sequence  may  be  broken  at,  or  near 
the  close,  in  order  to  gain  a  more  melodious  or  more  tuneful  pro- 
gression of  the  parts,  or  to  gain  a  more  satisfactory  close  in  any 
way.      See  seventh  measure  in  example  143. 

Sequences  are  said  to  be  tonal  or  diatonic,  when  intervals  are  re- 
peated in  the  same  key  without  regard  to  differences  in  the  quality 
of  the  intervals : 


-h — r*2^- 


Ex.  145. 


a     1  \/a 

%  o  *>  1  *> '-«?  ko  & 


J  U- 


g  : 


&-&*■&■ 


III! 


6^6  6 


gi^  .  h^  I-:  •!  j  11 


76 


PRACTICAL   HARMONY. 


Sequences  are  said  to  be  real  or  modulatory,  when  the  quality 
of  the  intervals  represented    by   the    model    is    exactly  repeated : 


Ex.  146. 


tisttaad 


-*=- 


-s>- 


-B>- 


6 

<2- 


9J=t 


dzte 


-S>- 


6 


m 


±=g 


1.^ 


±B: 


-<&- 


$ 


-!> 


:^g 


=t=F 


-te>— 


-s>- 


fe 


^ 


:te: 


It  is  recommended  that  the  pupil  play  the  following  exercises 
from  the  figured  bass,  instead  of  writing  out  the  other  voices  as  he 
has  done  heretofore.  The  position  of  these  voices  in  the  first  chord 
has  been  omitted  purposely.  As  the  greater  number  of  these  basses 
may  be  harmonized  in  two  or  more  positions,  the  pupil  should 
choose  that  position  which  seems  to  him  the  most  desirable. 


EXERCISES. 

TONAL    SEQUENCE. 


'•PP§@|SeIe3? 


->& 1- 


:Eees 


z± 


-a. 


II 


If5>         ,1—  £2— ° 


2-  \$^1rF3^F=i=f=£ 


-3—^2- 


2t 


! 


6  —  3 
6  6       4 


3.  m^^-^^Mimi^^R 


PRACTICAL    HARMONY. 


77 


6 

4  6 


>-^gg 


t=± 


"—& — <g 


-A- 


6 

4  6 


6 

4 


-&——&- 


~&- 


-& ,2_ 


4=t 


=1=1 


"5* «»— 


6 

4  6 


g 


2   b  * 


~G>—&— 

M 1_ 


-<S>— <2- 


6 

4  6  6 

-<9- 


~P-- 


.a.- 


1 


■  gfes 


b£=4 


£*=* 


rfEp 


:rf 


■#-*- 


F 


75^ 


I 


6 


.m 


—s)-&- 


f-* 


- 


&—&- 


=^_f2_-P_  P— ^. 


-f=2-£2s 


*= 


^H 


6  6         4 


7. 


33 


i^: 


3= 


6         6 
6  «      4 


^^P 


-P—&- 


^=? 


E3fet^ 


6  6            6 

6            4  _~           4 

--S--         _                       6                         6  -£2- 

-f2 — r<5» ?5 — i (S*- 


^=      gpEEg 


t=p 


6 
6  43 


E^i^=i 


8. 


3sa$ 


-(2- 


-(2- 


:t: 


-=1 


5-?- 


£ 


=t== 


-g»- 


-f2- 


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gllH 


-<S2- 


9.  ^j^=^E,=gE 


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-<5>- 


£==r 


-*+^-# 


H9-T- 


e 


10. 


Hg^ 


666666  66 

i=3 


*> 


t= 


o 


P 


£2 


1=*= 


=B 


n. 


gi3 


343  6  6  6  6  „  6  „ 

-O-.        3  43  34  3        343  343  343  6- 

-&-i—C 


—        ->    • 


;— :} 


o 


^- 


I 


6  6  6 

-~      6        4        6         ,,       6         4  6  6.     46, 


6 
4  3 


i2.immm^mw^\  i  *  1 1  - 1 1  g  n 


13. 


t)-  (• 


I    F^^TTTHr 


(-  ~r~  "^ — g* 


,->— l 


■i      * 


li 


78 


PRACTICAL    HARMONY. 
EXERCISES. 

REAL    OR    MODULATORY    SEQUENCE. 


1. 


;§±e 


°  i 


:p= 


«b  el)  sbebsbsb    5b6bobsbs!> 

b    sb  sb,  b     b     b      ,      b     b    4bb    b 


jf==r^rp^=»= 


b< 


I 


2. 


»JS=t 


-(2- 


:t 


5Q      5D  5j      5B       5fl      5fl  5Q 


* 


£=E 


5$ 


5$ 


3. 


;§3t 


-25f- 


-<s>- 


-<© 1 


1=F^: 


5$        5$ 

«  * 


6$  Srf 

4$$ 


5$ 

s 


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I 


The  student  should  now  compose  several  short  sequences,  both 
tonal  and  modulatory,  following  the  suggestions  given  on  pages  74 
and  75. 


CHAPTER   X. 

RESUME. 

Note.   In  this  concluding  chapter  of  Part  I.,  subjects  which  were 
purposely  treated  as  briefly  as  possible  in  the  preceding  chapters,  will 


PR  A  C  TIC  A  L    HA  RMONY. 


79 


be  discussed  more  fully.  Matter  which  would  have  there  been  cum- 
brous and  confusing,  will  here  be  useful  and  more  readily  under- 
stood. 

CHAPTER   I. 

At  example  14  it  was  stated  that  it  is  correct,  as  a  general  rule,  to 
use  sharps  in  ascending  passages  and  flats  in  descending  passages. 

Modern  writers  usually  choose  accidentals  which  are  nearest  in 
tonal  relationship  to  the  key  in  which  the  phrase  occurs. 

A  descending  passage  like  the  following: 


-s 


Ex.  147. 


-<& 


h. 


J=t 


-fS>- 


would  be  much  better  notated  thus  : 
Ex.  148. 


— \ 


=3=t 


-*— S*=ttfc 


-&>- 


because  the  FJJ  is  nearer  the  tonality  of  C  than  is  the  Gi?. 
The  same  would  be  relatively  true  of  the  following: 

Better  notation. 


Ex.  149. 


re=^g^gE|:|  jJE^g 


it*- 


"III 


In  our  musical  notation  we  recognize  no  interval  smaller  than  a 
semitone.  For  reasons  which  have  to  do  with  the  matter  of  temper' 
amcnt,  the  whole  step  is  theoretically  divided  into  nine  equal  parts 
called  the  Pytliagorcan  Commas.  The  comma  is  supposed  to  be 
the  smallest  appreciable  interval  between  two  sounds. 

Note.  The  terms  half-step,  and  semitone,  are  purposely  used  as 
synonyms. 

Of  the  nine  commas  dividing  any  whole  step,  that  portion  of 
them  representing  the  diatonic  semitone  is  the  smaller,  and  receives 
but  four  commas,  or  four-ninths  of  the  whole  step. 

The  chromatic  semitone  is  the  larger  and  receives  live  ninths  of 
the  whole  step. 

A  comma,  then,  or  one-ninth  <>t"  a  whole  step,  is  the  interval 
that  separates  the  diatonic  semitone  from  the  chromatic  semitone; 
i.e.,  it  is  the  difference  between  the  Hat  and  the  sharp  which  may 
separate  a  whole  step. 


So 


PRACTICAL   HARMONY. 
ILLUSTRATION. 


COMMAS     OfJE  Y/pOLE  STEP 


FIVE  COMMAS, 
CHROMATIC  (larSe)  HflLFSTEP 


COMMA 


I  COMMA 


2  COMMA? C0M"A 


4  COMMA  |5  COMMA  f 


FOUR  COMMAS, 


(i§       DlflTOfllC  (Small)  flflLFSTEP. 
6C0MMA,7COMMAr 


8C0MMA9 


FIVE  COMMAS, 


I    u  FIVE  COMMAS, 

FOUR  COMMAS,  [)  V  CHROMATIC  (LarSe)fiflLFS7E^, 

DIH  TO  Hie  (Small)  HflLF-STEPJ  \^^ 


WHOLE  STEP. 


On  instruments  of  a  fixed  sound,  like  the  piano  or  the  organ,  the 
whole  step  has  been  divided  into  two  equal  parts  by  a  system  known 
as  the  tempered  scale.  With  this  system  the  QJ  and  the  Di?  are 
identical. 

On  instruments  where  the  sound  is  formed  by  the  executant,  like 
the  violin  or  the  violincello,  the  musician  is  governed  by  melodic  in- 
stinct and  submits  involuntarily  to  the  fine  difference  existing  between 
the  flat  and  the  sharp,  making  use,  ordinarily,  of  the  large  half-step  in 
ascending  passages  and  the  small  half-step  in  descending  passages. 
If  this  is  understood,  the  student  will  realize  that  an  instrument  like 
the  piano  or  the  organ  is  never  perfectly  in  tune  when  played  with 
stringed  instruments.  The  difference  is  slight,  but  sufficiently 
marked  for  the  piano  to  sound  colorless  and  unsympathetic,  when 
entering  alone  after  a  full  passage  by  the  strings. 


CHAPTER    II. 
SCALES. 

The  chromatic  scale  is  composed  entirely  of  chromatic  and  dia- 
tonic semitones. 

Anv  major  or  minor  scale  may  be  transformed  into  a  chromatic 
scale  by  the  use  of  the  intermediate  semitones  which  separate  the 
whole  steps. 

These  intermediate  sounds  in  noway  imply  a  change  of  key,  and 
the  supreme  characteristic  of  the  chromatic  scale  may  be  said  to  lie 
in  the  fact  that  sharps,  flats,  or  naturals,  foreign  to  the  key,  may  be 
freely  introduced,  and  cause  no  sense  of  modulation. 


PRACTICAL   HARMONY. 
CHROMATIC  SCALE  OF  C. 


:x.  1 50.  J 


r73_^**=^ 


MS 


**+ 


m 


w 


8i 


or: 


{ 


55^3*3=*** 


K 


1 


g 


II 


Musicians  differ  as  to  the  best  notation  of  the  chromatic  scale. 
Composers  are  often  inconsistent,  at  one  time  writing  the  ascending 
series  with  sharps,  at  another  time  with  flats.  As  a  note  sharped  is 
nearer  the  semi-tone  above  than  the  note  quitted,  it  would  seem 
to  be  the  better  notation  to  use  sharps  in  the  ascending  major  scale 
and  flats  in  the  descending  scale.  An  important  exception  is  made 
in    the    flatted    seventh    in    ascending,    and    the    raised    fourth    in 


descending. 


The  chromatic  scale  in  minor  is  usually  written  as  follows: 
Ex.  1  52.'^2tM^_gEp^EibzE   -P^MH^lrlzpzp^iffibL} 


The  question  of  the  notation  of  the  chromatic  scale  is  one  on  which 
there  is  great  diversity  of  opinion.  Conditions  have  so  much  to  do 
in  determining  which  shall  be  written,  sharps  or  flats,  that  it  would 
seem  wiser  to  attempt  no  inflexible  ride. 

No  further  proof  of  the  inconsistency  of  musicians  ;is  regards  the 


8s 


PRACTICAL   HARMONY. 


notation  of   the   chromatic   scale,  need  be  given,  than   the  follow« 
ing  example  by  Beethoven  : 


Ex.  153. 


ssgggggjilili 


About  the  only  thing  on  which  composers  seem  to  agree,  is  in 
writing  the  fourth  note  sharped  in  the  ascending  major  scale,  and 
the  seventh  note  flatted  in  the  descending  scale.  (  For  an  expla- 
nation of  this,  see  examples  147  and  149.)  This  done,  they  evidently 
think  of  the  convenience  of  the  performer.  It  should  be  understood 
that  we  are  now  discussing  chromatic  melody.  Chromatic  harmony 
will  be  considered  later. 


THE  ECCLESIASTICAL  SCALES. 
The  "  Gregorian  Tones,"  "  Church  Modes"  or  '•''Ecclesias- 
tical Scales"  as  they  are  variously  named,  are  of  Greek  origin.  If 
the  student  will  play  a  scale  from  each  note  of  the  scale  of  C,  using 
white  keys  only,  he  will  obtain  the  seven  different  forms  of  these 
Church  Modes,  or  scales,  as  they  would  now  be  called.  Each 
mode  has  a  different  order  for  its  steps  and  half-steps.  As  many 
pupils  have  a  desire  to  know  something  about  these  scales,  we  add 
the  following  typical  list : 


The  Dorian,  or  First  Mode 
F.  D. 

-J 


The  Hypo-Dorian,  or  Second  Mode. 
F.  D. 


The  Phrygian,  or  Third  Mode. 
F.  D. 


The  Hypo-Phrygian,  or  Fourth  Mode. 
F.  D. 


2^| 


The  Lydian,  or  Fifth  Mode. 
F.  I). 


-&~ 


^JESE^g-l  E 


The  Iiypo-Lydian,  or  Sixth  Mode. 
F.  D. 


h=+=l=± 


r> 


^m 


The  Mixo-Lydian,  or  Seventh  Mode.    The  Hypo-Mixo-Lydian,  or  Eighth  Mode. 
F.  1).  F.  1). 


0     • 


*> 


HiEliipli 


^ 


3 


d: 


^ 


•J] 


PRACTICAL   HARMONY.  S3 

It  will  be  seen  that  the  Ecclesiastical  Modes  are  formed  of  the 
notes  of  our  scale  of  C,  each  starting  from  a  different  degree. 
These  scales  are  grouped  in  pairs,  so  to  speak.  The  first,  third, 
fifth,  and  seventh  modes  are  termed  Authentic.  Each  of  these  has 
a  collateral  mode  at  the  interval  of  a  fourth  below ;  they  are  distin- 
guished by  the  prefix  Hypo  (  under  ) .  The  Hypo  modes  are  termed 
Plagal. 

It  would  seem,  at  first  glance,  that  if  harmonies  were  formed  on 
these  different  modes,  without  the  use  of  accidentals,  the  general 
tonal  effect  would  be  the  same  as  our  key  of  C  major. 

These  modes  are  characterized,  however,  not  only  by  the  different 
order  of  intervals  in  each,  but  by  the  constant  recurrence  of  two 
chords,  called  the  Final  and  Dominant,  corresponding  to  our  Tonic 
and  Dominant.  It  is  the  insistence  of  these  two  chords  which  makes 
each  mode  distinct.  These  chords  are  designated  by  a  whole  note 
in  the  preceding  list  of  scales.  The  Final,  or  Tonic,  is  marked 
with  an  F,  the  Dominant  is  marked  with  a  D.  It  will  be  noticed, 
that  although  the  order  of  intervals  in  the  Hypo-Lydian  corresponds 
to  our  major  scale,  the  points  of  repose  coming  on  F  and  A  remove 
it  farther  from  our  idea  of  key,  or  tonality,  than  either  the  Lydian 
or  the  Mixo-Lvdian.  In  order  to  avoid  the  relation  of  the  tritone, 
the  B  is  sometimes  flatted.  If  B  were  flatted  in  harmonies  in  the 
Lydian  Mode,  the  tonal  effect  would  be  much  like  our  major  mode. 
This  svstem  was  later  extended  to  fourteen  modes. 

Modern  composere  have  at  times  employed  these  scales  with 
good  effect.  Handel  has  made  frequent  use  of  them  in  his  ora- 
torios. Saint-Saens  and  Brahms  have  employed  them  with  charm- 
ing results. 

CHORDS. 

The  terms  chord  and  triad  have  been  intentionally  used  as  synony  im 
in  the  preceding  chapters.  A  triad  is  always  a  chord,  but,  as  will 
be  seen  in  Part  II.,  a  chord  may  be  larger  than  a  triad. 


TRIADS. 

Tiic  triad,  or  chord  of  three  sounds,  forms  the  essentia]  and 
indispensable  element  of  harmony.  Until  the  close  of  the 
sixteenth  century,   this  chord,   united  to  certain  effects  known  as 


S4  PRACTICAL    HARMONY. 

"artifices  of  composition,  "  to  be  explained  later,  was  the  only  one 
used. 

The  triad  on  the  leading-tone,  although  classed  by  some  theorists 
as  an  independent  triad,  is  classed  by  the  greater  number,  and  by  all 
the  modern  French  theorists,  as  an  incomplete  dominant  7th  chord. 
This  will  be  fully  explained  In  Part  II.  A  triad  formed  on  any 
note  of  the  major  scale,  except  the  leading-tone,  is  consonant,  and 
may  be  used  as  a  tonic.  For  example,  any  triad  in  the  key  of  C 
when  standing  alone  will  be  accepted  by  the  ear  as  a  tonic,  either 
major  or  minor,  according  to  the  degree  on  which  it  is  formed. 
In  other  words,  they  all  are  consonant  chords ;  they  give  a  sense  of 
tepose,  requiring  nothing  to  follow  them. 

The    triad    on    the    leading-tone,    on    the  contrary,   is,   with  its 

Uminished  fifth,  distinctly  dissonant  :— 


-73- 


1 


'•id  in  no  sense  gives  the  feeling  of  repose  or  finality :  something 
'~ust  follow  it. 

This  triad  in  its  first  inversion,  was  classed  among  the  concords 
I  the  so-called  ancient  strict  style  : 


Ex.  154.< 


-73- 


6 


-G>- 


;H 


This  inverted  chord  was  often  written  by  early  composers  in 
preference  to  the  dominant  chord.  This  will  be  understood  when 
Ihtj  true  generator  of  the  chord  has  been  discussed. 

This  leading-tone  triad  in  its  first  inversion  seems  to  be  the  con- 
necting link  between  the  strict  style  and  the  free;  the  bridge 
over  which  one  passes  from  the  old  to  the  new.  It  contains 
no  diminished  nor  augmented  interval  from  the  bass,  nor  the 
interval  of  a  fourth  from  the  bass,  yet  it  possesses  all  the  distin- 
guishing characteristics  of  a  dissonance  as  explained  in  Chapter 
VII. 


J'RA  C  TIC  A  L    HA  RAW  NY. 

OMISSION    OF    VOICES. 


*> 


The  third  of  the  dominant  chord  is  often  omitted.  As  the  third 
of  this  chord  is  always  major  in  cither  mode,  its  suppression  causes 
no  ambiguity.  Passages  like  die  following  are  of  frequent  occur- 
rence and  entirely  satisfy  the  ear : 


^=F(k)g 


Ex.  155. 


The  omission  of  the  third  of  any  chord  other  than  the  dominant, 
by  very  reason  of  its  ambiguity  and  strangeness,  has  a  particularly 
pungent  effect.      This  is  especially  true  of  a  tonic  : 

String  Quartette 
Ex.  1  56. 


MELODIC    PROGRESSION. 


Students  often  ask  why  the  apparently  easy  interval  of  the  major 
sixth  is  forbidden.  Experience  proves  that  this  interval  is  difficult 
of  correct  intonation  unless  another  voice  has  anticipated  it  in  the 
preceding  chord : 


Ex.  157 


1 


II 


-<s~ 


-&- 


& 


II 


or  unless  the  progression  is  from  the  tonic  to  the  sixth  degree: 

lUi 


Ex,  1  58. 


S6 


PRACTICAL    HARMONY. 


CONSECUTIVE    FIFTHS    AND    OCTAVES. 

As  little  as  possible  has  been  said  about  these  so-called  forbidden 
intervals,  for  the  reason  that  so  much  attention  is  given  to  them  in 
the  average  text-book  on  harmonv  that  the  student  imagines  an 
octave  or  fifth  in  every  possible  progression. 

Consecutive  fifths,  and  octaves  by  contrary  motion,  are  found  in 
the  compositions  of  the  best  composers  : 


Pastoral  Symphony. 


Beethoven. 


Ex.  159 


S 


Passages  like  the  preceding  should  not  be  imitated,  but  they 
prove  that  after  one  has  gained  sufficient  technique  he  may  make  a 
good  effect  out  of  material  which,  in  the  hands  of  the  inexperi- 
enced, is  crude  and  distasteful. 


HIDDEN    FIFTHS. 

When  two  notes  move  in  similar  motion  to  a  fifth,  as  at  a  and  l>, 
Ex.  1 60,  the  voices  pass  over  notes  which,  if  written  out,  would 
produce  consecutive  fifths : 

a.  b. 

160. 


Ex. 


i—g L 


-4- 


o 


r 


Such  progressions  are  called  hidden  fifths.  They  are  oftentimes 
as  disagreeable  as  the  consecutive  fifths  which  they  suggest.  Like 
all  other  questionable  progressions,  they  are  most  disagreeable  be- 
tween outside  voices.  Hidden  fifths  or  hidden  octaves  are  usually 
unobjectionable  between  outside  voices  if  the  upper  voice  moves 
diatonically  and  the  lower  voice  by  a  skip. 


^\ 


Midden  fifths.       Hidden  octaves. 


Ex.  161. 


^*-r 


:E: 


II 


PRACTICAL    HARMONY. 
THE    TRITONE. 


87 


If  what  was  written  under  Ex.  129  concerning  the  tritone,  is 
thought  too  sweeping,  one  need  only  consult  the  various  text-books 
on  harmony  and  counterpoint  to  rind  the  most  obscure  and  contra- 
dictory rules.  The  essential  tiling  is  to  understand  how  to  grain  tiie 
good  effect  and  avoid  the  bad.      The  following  is  sufficient. 

Avoid  the  relation  of  the  tritone  between  outside  voices,  in  the 
progression  from  the  fifth  degree  to  the  fourth  degree. 

The  progression  from  the  fourth  degree  to  the  third  degree  also 
contains  the  tritone,  but  this  progression  is  disagreeable  under  any 
conditions  and  should  be  avoided. 


CHAPTER   III. 

SCALES.     THE    MINOR    MODE. 

In  addition  to  the  harmonic  minor  scale  as  given  in  Chapter  III., 
there  are  other  forms,  the  most  used  of  which  is  the  one  called  the 
melodic  minor.     It  is  formed  as  follows : 


Ex.  162. 


i 


-<s>- 


•5- 


-(5>- 


-gs?-&g— -flg-gg- 


<5 


-f9- 


#-zzA\ 


I 


This  form  of  the  minor  scale  with  its  seventh  flatted  in  descend- 
ing, permits  the  use  of  the  melodic  progression  from  the  seventh 
degree  to  the  sixth  degree,  which  is  objectionable  in  the  harmonic 
minor  scale,  on  account  of  the  augmented  second : 

Mendelssohn. 

Ex.  163. 


THE    AUGMENTED    SECOND. 


The  interval  of  the  augmented  second  is  musical,  and  one  of  the 
most  expressive  in  the  whole  category  of  intervals.  It  is  used  by 
composers  as  an  expression  of  strong  emotion,  and  is  so  frequently 
and  freely   used    by    modern   composers,  that    it    seems  unwise  to 


ss 


PRACTICAL  HARMONY. 


forbid  its  use  unconditionally.  Unless  carefully  introduced  it  is 
difficult  of  intonation,  and  for  that  reason  it  has  been  forbidden  by 
the  majority  of  theorists.  It  is  much  easier  to  sing  as  an  ascend* 
itig  interval  than  as  a  descending,  and  may  be  used  occasionally 
when  the  second  note  is  leading-tone  moving  to  tonic : 


Ex.  164. 


-^ 


J 


I <2_ 

a* 


-G>- 


— %>- 


--&- 
--&- 


i — &. 


I 


i 


This  interval  should  be  introduced  rarely  and  then  confined 
almost  wholly  to  solo  voices. 

In  the  minor  mode  the  melodic  interval  of  an  imperfect  fourth  i? 
permitted  when  the  second  note  is  leading-tone  moving  to  tonic : 

4- 


Ex.  165. 


I 

t 


9- 


-©>- 


-&■- 


-&- 


This  same  interval,  moving  from   the  leading-tone  to  the  Laird 
decree,  is  often  foimd  in  the  writings  of  Bach  : 


Ex.  1  66. 


I 


v.  *?: 


-<s> — ' — g>- 

'-(9- 


II 


Note.  (See  note  and  Ex.  53,  page  26.)  The  aversion  of  the 
early  composers  to  an  ending  with  a  minor  third  was  so  strong, 
that  the  third  of  a  final  chord  was  often  altogether  omitted,  and  3 
close  made  as  follows : 


Ex.  167 


II 


PRACTICAL    HARMONY. 


39 


This  close  is  found   in  modern    compositions  where    there  is  a 
wish  to  suggest  the  archaic  character  of  these  earlier  writers. 


CHAPTER   IV. 

CHORD-RELATION. 

TONALITY. 

By  tonality  is  meant  a  succession  of  tones,  either  melodic  or 
narmonic,  sufficiently  long  to  clearly  establish  a  certain  key.  When 
one  hears  such  a  succession  the  musical  sense  instinctively  clusters 
these  tones  around  one  principal  tone,  or  point  of  repose,  which  we 
call  tonic.  Taking  all  the  tones  which  affirm,  so  to  speak,  this 
tonic,  and  we  have  a  scale  ;  taking  the  chords  found  on  the  different 
degrees  of  the  scale,  and  we  define  or  make  clear  the  tonality  of  a 
key. 

An  appreciation  of  the  laws  of  tonality  is  of  the  greatest  impor- 
tance. Without  it  many  of  the  great  works  of  the  modern  school 
seem  obscure  and  keyless.  The  student  will  remember  that  "the 
supreme  characteristic  of  the  chromatic  scale  lies  in  the  fact  that 
sharps,  flats,  or  naturals  foreign  to  the  key  may  be  freely  introduced 
and  cause  no  sense  of  modulation.  "  That  which  is  true  of  chromatic 
melodic  passages,  is  equally  true  of  chromatic  harmonic  passages. 
Here  will  be  found  one  clue  to  an  understanding  of  the  modeiv 
school. 


CHAPTER   VI. 
THE    FIRST   INVERSION. 
The  first  inversion  is  so  agreeable,  that  when  moving  to  it  many 
hidden   fifths  and  octaves,  which  would  be  forbidden  if  the  chord 
stood  in  its  fundamental  position,  are  unobjectionable  : 


Ex.  168 


i 


c 


o> 


6—  »t 


C 


_-§:- 


'( 


& 


—6- 


II 


qq  PRACTICAL   HAN  MO  NY. 

CHAPTER   VIII. 

FORM. 

The  study  of  form  is  most  necessary.  It  is  a  branch  by  itself, 
and  no  attempt  was  made  in  Chapter  VIII.  to  do  more  than  barely 
define  it.  Musical  compositions  are  divided  into  two  principal 
forms,  each  essentially  distinct  from  the  other;  one  is  the  Fugal 
or  Canonic,  the  other  is  the  Metrical.  The  fugal,  on  account 
of  the  irregularity  of  its  members  and  development  of  its  periods, 
together  with  various  artifices  of  composition  which  do  not 
permit  the  regular  return  of  the  cadences,  may  be  compared  to 
prose;  it  appeals  to  the  more  cultured  mind.  The  metrical,  bv  its 
frequent  and  regular  return  of  cadences  and  corresponding  members, 
approaches  nearer  verse;  it  impresses  itself  more  readily  on  the 
memory  than  the  fugal.  Since  the  beginning  of  the  eighteenth  cen- 
tury the  greatest  composers  have  united  both  the  fugal  and  the  metrical 
in  their  more  important  works.  This  combination  is  found  in  all 
its  splendor  in  the  works  of  Bach.  The  student  cannot  become 
too  familiar  with  the  compositions  of  this  unparalleled  genius 
Charles  Gounod  said  :  "  Bach  is  in  music  a  star  of  the  first  magni- 
tude :  like  Dante,  Shakespeare,  and  Michael  Angelo  he  marks  one 
of  those  summits  reached  but  once  in  the  history  of  one  art ;  he  alone 
has  laid  the  foundations  of  the  music  of  the  future.  His  work 
already  dates  more  than  two  centuries ;  time  cannot  alter  it,  and  tar 
from  being  surpassed  no  one  has  equalled  its  bold  invention  or 
its  dignity  of  style.  His  language  has  a  biblical  grandeur  recalling 
that  of  the  prophets. 

"But  that  which  cannot  be  too  strongly  emphasized  is  that  his 
incomparable  audacity  is  a  direct  result  of  his  severe  discipline, 
and  that  there  is  not  a  caprice  of  his  marvelous  fantasy  which  may 
not  be  resolved  to  the  most  simple  elements  and  be  explained  by 
the  most  rigid  principles. 

"  We  cannot  too  strongly  recommend  the  young  musician  to  read 
and  re-read  the  works  of  Bach;  more  than  that,  we  urge  him  to 
learn  some  of  the  most  remarkable  passages  by  heart. 

"  The  young  musician  generallv  underestimates  the  importance  of 
having  constantly  before  him  models  of  the  great  masters.  If  he 
fears  that  in  memorizing  their  works  lie  will  lose  his  individuality, 
he  does  not  reflect  that  the  study  of  a  master  always  brings  us  into 
the  presence  of  two  elements,  — that  which  the  master  knows,  and 


PR  A  C  TIC  AL   HA  KMONY. 


9* 


that  which  he  is,  and  that  of  these  two  elements  —  united  in  the 
master — -the  first  only  is  communicable  and  can  be  assimilated. 

"Art  is  subject  not  only  to  grammatical  rules,  to  principles  of 
correction  without  which  there  would  be  a  fault,  but  also  to  princi- 
ples of  beauty,  to  laws  of  aesthetics,  which,  although  they  may  not, 
like  the  former,  be  reduced  to  rules,  are  no  less  sure  and  positive,  and 
which  constitute  the  chain  by  which  all  the  great  masters  are  united  ; 
grand  laws  by  virtue  of  which  Dante,  Shakespeare,  Michael  Angelo, 
Bach,  and  Palestrina  are  all  one  family." 

Cherubini  also  urges  the  student  "to  read,  and  also  carefully 
and  thoughtfully  to  copy  as  much  as  possible  the  works  of  classic 
composers.  By  this  practice  the  student  will  train  the  ear  by  the 
eye,  and  his  taste,  sentiment,  and  style  will  be  progressively 
formed." 

CHAPTER  IX. 

MODULATION. 

Modulation  will  form  an  important  feature  of  Part  IT.  The 
examples  contained  in  Chapter  IX.  are  not  sufficient  to  enable  one 
to  analyze  modern  music.  The  term  "closely-related  keys"  is 
misleading.  Examples  are  numerous  in  works  by  modern  masters, 
in  which  beautiful  modulations  are  made  to  keys  supposed  to  be  the 
most  remote  from  the  original  tonic.  As  these  modulations  neither 
shock  the  ear  nor  destroy  the  sense  of  unity,  it  must  be  admitted 
that  there  is  a  relationship  existing  between  all  keys. 

A  theory  may  claim  that  there  is  no  relationship  existing  between 
kevs  of  which  the  tonics  are  dissonant,  and  yet  the  student  will  find 
countless  examples  in  which  melodic  and  harmonic  material  is  used 
in  keys  said  to  be  unrelated,  and  used  in  a  way  which  proves  that 
there  is  a  relationship. 

The  question  is  one  of  aesthetics,  and  not  one  that  can  be  settled 
by  laws  of  acoustics,  or  explained  by  the  so-called  "harmonic  series" 
or  "overtones."  "The  exactitudes  of  science  and  Art  ideals  have 
nothing  in  common." 

Part  I.  closes  here.  As  consonant  harmony  is  the  basis  of  all 
harmony  whatsoever,  it  is  important  that  it  should  be  well  mastered 
before  taking  up  dissonance.  The  teacher  must  be  the  judge  as  to 
whether  or  not  certain  lessons  should  be  reviewed. 

END     OK     PART     I. 


STUDENTS'   HARMONY 

. . . BY  . . . 

ORLANDO  A.  MANSFIELD,  Mus.  Doc. 


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CONCISE  AND  EASILY  UNDERSTOOD 

A    SYSTEM    OF    TEACHING 

HARMONY 

The  Standard  Text-Book  of  Musical  Theory 

By   HUGH  A.  CLARKE,  Mus.  Doc. 

of  University  of  Pennsylvania 

The  Object  kept  in  View  is  how  to  enable  the  pupil  to 
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39 


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44 


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memory. 

It  can  be  used  very  advantageously  by  the  student  who  is 
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HARMONY  AND  COMPOSITION 

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A   Practical   Course   in   Harmony   and 
the  Elements  of  Musical  Composition 

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stood works  on  harmony  of  which  we  know,  written  by  an 
American  for  American  students,  not  a  translation  from  a 
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49 


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